 1770 FIN312.HLP, Generated by A3UTIL.EXE, 1994  (c) PCSCC Inc., 1993,01#9LÇ▀à╜Θ
cä╙3╞_≡#9PÆªUû┐╘                                                                                                                                                    ┌───────┐          Interactive Problem Solving in                       │FINANCE│                                                               │ ┌─────┴─┐            FINANCIAL CALCULATIONS                           │ │ANNUITY│                                                             └─┤ ┌─────┴─┐       Using AstroFormulaCalculator 3                        │ │ BONDS │                                                             └─┤ ────- │    Application File  Version 3.12   03-01-1994                │ ────- │                                                               └───────┘                                                                                by  P. DuBois Murphy, Ph.D.                                                                                                                                                                          (c) Copyright 1981, 1994  PC SuperComputer Capital, Inc.                                                                                                            All rights reserved.                                                                                                    Before using, please read  WARRANTY INFORMATION . Type J to read.                                                                             Instructions on using help file are at end of file. Type K to read.                                                                                                                                                   ╒══════════╕                                                            │ CONTENTS └──────────────────────────────────────────────────────────                                                                          0.00                  Table of Contents                                                                                                               *    To quickly jump to Sections, position the Section line number      *    on the │JUMP│ line (line 12) and type J or type Lxxx (enter)       *    where xxx is line number. For example, to jump to line 139,        *    type L139 (ent).  Type S or R to skip back/forth to Sections.                                                                         SECTION                   TITLE                              PAGE│LINE                                                                           0.00 ... Table of Contents ................................... 1   27  1.00 ... Introduction ........................................ 2   72  2.00 ... Personal Finance: An Introduction to Financial ...... 3  124           Calculations                                                   3.00 ... Progressions (Arithmetic and Geometric) and ......... 5  219           Depreciation                                                   4.00 ... Simple Interest. .................................... 9  385  5.00 ... Simple Discount. ................................... 10  441  6.00 ... Partial Payments. .................................. 11  485  7.00 ... Compound Interest. ................................. 12  521  8.00 ... Compound Interest, Present Value, Equation of ...... 14  607           Value.                                                         9.00 ... Ordinary Annuities Certain ......................... 14  640  10.0 ... Amortization and Sinking Funds ..................... 16  719  11.0 ... Bonds .............................................. 18  815  12.0 ... Annuities Due, Deferred Annuities, Perpetuities .... 21  962  13.0 ... Annuities Certain, General Case .................... 23 1026  14.0 ... Probability and the Mortality Table. ............... 25 1115  15.0 ... Life Annuities ..................................... 28 1260  16.0 ... Useful Calculations for Problem Solving in ......... 29 1311           Finance.                                                       17.0 ... Glossary of Terms .................................. 29 1333  18.0 ... Product License and Warranty. ...................... 30 1356  19.0 ... User Support. ...................................... 31 1422  20.0 ... Product Information and How to Order Complete ...... 32 1442           Package.                                                       21.0 ... Software Included in Astro 3 Registration .......... 34 1532  22.0 ... Order/Registration Form ............................ 36 1617  23.0 ... Instructions for Manually Installing Package. ...... 37 1682  24.0 ... Interested in Becoming the Author of Your Own ...... 38 1723           Interactive Application File?                                  25.0 ... Help File: Summary of File Viewing Commands ........ 38 1744                                                                        ╒═══════════════╕                                                       │ INTRODUCTION  └──────────────────────────────────────────────────────                                                                         1.00          Introduction                                              ────────────────────────────────────────────────────────────────────────                                                                                 This document is an on-line application file which discusses            the theory and presents solved problems in finance such as in           interest, in annuities, in bonds and so on.  An excellent               reference, which can serve both as a supplement to an existing          course in finance or as a stand-alone study or self-help guide,         is the book:                                                                                                                                             "Mathematics of Finance"                                                 Frank Ayers, Jr.                                                        Schaum Outline Series in Business                                       McGraw-Hill Book Company, New York                                      1963                                                                                                                                  While over 30 years old at the present time, Dr.  Ayers' book           still presents a comprehensive and remarkably clear discussion          of the basic financial concepts.                                                                                                                Personal computers (PC's) and their automation and calculation          capabilities were not available back then.  For example, pages          of traditional tables for compound interest and annuities with          "eight decimal places" are simply not needed.  Proper use of            the PC can reduce or eliminate much of the tedium associated            with reducing theory into algebraic expressions and then into           useful day-to-day applications.                                                                                                                 This PC application file is intended to provide students of             finance with help in mastering the execution of the necessary           algebra and math calculations upon which finance is heavily             based.  The application is driven by a versatile                        spreadsheet/calculator call AstroFormulaCalculator 3 which              exists as the file ACAL3.EXE.  This program is specifically             tailored for analysis based on algebraic expressions, formulas          or equations.  One of its main functions is to eliminate the            "programming-type overhead" in working with known formulas and          to allow meaningful learning to proceed rapidly.                                                                                                AstroFormCalc 3 can be used with any traditional outline manual         or text to develop equation templates that solve specific               problems.                                                                                                                                       This file is organized by topics with are summarized in the             Table of Contents.  The use of AstroFormCalc 3 is discussed in          the on-line help file which is accessed by typing (F1) from the         equations display.  This entire file can be searched using the          auto-search command "A".                                                                                                               ╒══════════════════╕                                                    │ PERSONAL FINANCE └────────────────────────────────────────────────────                                                                        2.00 Personal Finance: An Introduction to Financial Calculations        ────────────────────────────────────────────────────────────────────────                                                                                 This Section describes some common financial calculations that          are relevant to most people:  home mortgage refinancing, zero           coupon bond, deferred annuity and negative amortization.  One           does not have to be a financial whiz in order to use these              calculations.  All that one needs is the ability to identify            what financial numbers are associated with what financial               variables.  The text associated with each calculation describes         an application.  The first-time user need only relate what is           presented to a similar situation.                                                                                                             ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 1: AMORTIZATION, SAVINGS ON REFINANCING A HOME MORTGAGE                                                                                 Discussion: Mary and Bill Smith are refinancing their home mortgage      ($102,400 at 14.75% nominal for 30 years) after 5 1/2 (5.5) years with  a new 30 year mortgage at 7.5% nominal plus 2 points and $1200 of       closing costs. What is their monthly savings? (b) What is there         nominal (before taxes, etc.) interest savings if they hold their new    mortgage for 24.5 years.?                                                                                                                      'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINCREF2      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          A zero coupon bond is a bond without a nominal interest rate            that pays its nominal or face value FACEVAL at maturity in              TERMYRS years.  It is similar to a treasury bill because it is          purchased at a price PURPRICE which has a steep discount from           its face value.  'Interest' payments are usually added to the           present value twice each year (semiannually).  Because it lacks         a nominal interest rate, for tax purposes, one must calculate a         yearly interest throughout its lifetime of TERMYRS.  In the             following treatment a nominal annual, or simple, interest rate          ANNRATE% is calculated for the 'zero' assuming that the                 purchase price will grow to the face value with semiannual              compounding.                                                                                                                                    The problem described below can be used to estimate the amount          of interest one should report as taxable income for a 'zero'.                                                                                 ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 2: ZERO COUPON BONDS                                                                                                                    Problem # 2.1: Mr. Jones estimates that he will need $60,000 to pay for  his newly-born daughter's college education in 18 years. He purchases   60 $1,000 'zeros' which mature in 18 years on the open market for $16,  325 on July 1st.                                                        (a) What should he report as interest income for the first year         YEAR#=0.5?                                                              (b) What must he report as interest income for the second year          (YEAR#=1.5)?                                                                                                                                   'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINCZER2      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 3: ORDINARY DEFERRED ANNUITY: SETTING UP A RETIREMENT FUND                                                                              Problem # 3.1: Mr. Lew has just turned 40. He wants to set up a          retirement fund which will pay him a monthly income of $1,000 begining  at age 65 and continuing each month for 20 years, his projected life    span. Money is worth 7% effective.                                      (a) How much will it cost him to purchase this deferred annuity?                                                                               'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINCDEF2      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 4: NEGATIVE AMORTIZATION, ADJUSTABLE RATE MORTGAGE, ARM                                                                                 Problem # 4.1:                                                           (a) What are the negative amortization rates for a $100,000, 30 year,   7.5% loan after payments # 1, 60 (5 yrs), 120 (10 yrs), 240 (20 yrs)?                                                                          'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINCNEG2      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          The remainder of the on-line manual studies many basic concepts         which when grouped together are commonly called the                     "Mathematics of Finance".  Remember, while in the equations             display, type (F2) to return to this application file.                                                                                 ╒══════════════╕                                                        │ PROGRESSIONS └────────────────────────────────────────────────────────                                                                        3.00       Progressions (Arithmetic and Geometric) and Depreciation     ────────────────────────────────────────────────────────────────────────                                                                                 A progression is a sequence of numbers, called TERMS, in which          any term can be obtained from its predecessor by adding,                subtracting, multiplying by or dividing by a fixed number.              When terms are generated by adding/subtraction a fixed number           called the COMMON DIFFERENCE, the progression is called                 ARITHMETIC.  When terms are generated by multiplying/dividing           by a fixed number called the RATIO, the progression is called           GEOMETRIC.  Many financial calculations are based on the                concept of the progression.                                                                                                                     The following examples illustrate an arithmetic progressions            with common differences of 4 and a geometric progression with a         common ratio of 2, respectively, between terms.                                                                                        ----------------------------------------------------------------------- Arithmetic progression: 4, 8, 12, 16, ...   (common difference = +4)                                                                            com. diff.       +4 =   +4 =   +4 =   +4 =    +4 =    +4 =    +4 =                                                                              term           4      8     12     16     20      24      28      32 ...                                                                        index          1st    2nd   3rd    4th    5th     6th     7th     8th   -----------------------------------------------------------------------                                                                         ----------------------------------------------------------------------- Geometric progression: 4, 8, 16, 32, ...   (common ratio = +2)                                                                                  com. ratio       *2 =   *2 =   *2 =   *2 =    *2 =    *2 =    *2 =                                                                              term           4      8     16     32     64     128     256     512 ...                                                                        index          1st    2nd   3rd    4th    5th     6th     7th     8th   -----------------------------------------------------------------------                                                                                  Some problems that illustrate the concepts of progressions              follow.                                                                                                                                       ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 5: ARITHMETIC PROGRESSION                                                                                                               Problem # 5.1:                                                           (a) Find the 12th term and the sum of the first 12 terms of the         arithmetic progression 30, 55, 80, 105 ...                              (b) Find the sum of the first 15 terms of the arithmetic progression    108, 100, 92, 84...                                                                                                                            'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC3P1       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 6: GEOMETRIC PROGRESSION                                                                                                                Problem # 6.1:                                                           (a) Find the 10th term and the sum of the first 10 terms of the         geometric progression 20, 40, 80, 160 ...                               (b) Find the sum of the first 12 terms of the geometric progression 8,  -16, 32, -64...                                                                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC3P2       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          DEPRECIATION is a loss in value of physical assets (tools,              cars, buildings, etc.) through use.  The methods used to                determine the annual depreciation charge are somewhat arbitrary         and are open to objections.  Some methods are:  the                     straight-line method (SLM), constant percentage method (CPM),           and so on.  The CPM is based on a GEOMETRIC PROGRESSION and the         successive book values over the life of the asset are the terms         of the progression.  A graphical comparison of the CPM and the          SLM follows.  Notice how the book value drops off more steeply          with the CPM (based on a geometric progression) than with the           SLM.                                                                                                                                                                                                          40 -*b <------- Original cost              Depreciation of asset.        | d b Book value vs. time (in years)                                      |   d   b                               Original cost = $40             |     d     b                           Scrap Value = $4                |       d       b                       6 year depreciation term     31 -        d        b                                                     |          d          b                                                 |            d            b                                             |              d             b                                          |                d              b     <----- Straight line method    22 -                  d                b                                   |                     d                 b                               |                        d                 b                            |                           d                 b                         |                              d                  b                  13 - Constant percentage method --->  d                  b                 |                                      d                b               |                                           d               b           |                                                 d             b       |                                                        d   d  d  b  4 -  <--- Scrap value --------------------------------------------> d     ||--------------|--------------|--------------|--------------|------     0             1.3            2.6            3.9            5.2                                       Time in years (N)                                                                                                       The equation templates for both the CPM and the SLM follow.                                                                                   ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 7: DEPRECIATION, CONSTANT PERCENTAGE (RATE) METHOD                                                                                      Problem # 7.1:                                                           (a) A car costing $19,200 has a useful life of 6 years and has a scrap  value of $1,440. Find the annual rate of depreciation.                  (b) Construct a depreciation schedule: book value at year end,          depreciation charge and amount in depr. fund for years 1, 3 and 6.                                                                             'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC3P3       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          The problem described below contains applications of the                straight-line (SL), doubly-declining balance (DDB) and                  sum-of-the-years-digits (SYD) methods.                                                                                                 Topic # 8: FINANCE: DEPRECIATION, STRAIGHT LINE, DOUBLE-DECLINING-       BALANCE, SUM of the YEARS DIGITS METHODS                                                                                                       Discussion: Calculate and compare the depreciation charges using the     straight-line, double-declining-balance and the sum-of-the-years        digits methods for an item costing $8,000 new at 1, 3 and 6 years over  a 10 year depreciation.                                                                                                                        'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINCDEPR      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          INFINITE GEOMETRIC PROGRESSION.  A geometric progression for            which the magnitude of the common ratio is less than 1.0 is a           called an infinite geometric progression.  The common ratio is          always greater than -1.0 but less than +1.0.  The most                  prominent property of an infinite geometric progression is that         it always has a finite value even when the number of terms get          extremely large, or approach infinity.                                                                                                        ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 9: INFINITE GEOMETRIC PROGRESSION                                                                                                       Problem # 9.1:                                                           (a) Find the sum of the infinite geometric progression: 16, 8, 4, 2.... (b) Find the sum of the infinite geometric progression: 16, -4, 1, -.   25....                                                                                                                                         'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC3P4       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═════════════════╕                                                     │ SIMPLE INTEREST └─────────────────────────────────────────────────────                                                                        4.00       Simple Interest.                                             ────────────────────────────────────────────────────────────────────────                                                                                 INTEREST is money paid for the use of a principal (borrowed             money) or money earned when a principal (investment capital) is         invested.  A basic assumption of the mathematics of finance is          that money is always invested productively.                                                                                                   ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 10: INTEREST, SIMPLE INTEREST and RATE OF INTEREST                                                                                      Problem # 10.1: Mr. B borrows $2000 from Mr. L and at the end of one     year pays Mr. L $2400.                                                  (a) What is the interest earned by Mr. B and                            (b) what is the interest rate Mr. B. charges Mr. L.?                                                                                           'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC4P1       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          SIMPLE INTEREST.  When only the principal earns interest for            the entire term of the transaction, the INTEREST due at the end         of transaction is called SIMPLE INTEREST.                                                                                                     ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 11: EXACT SIMPLE INTEREST, ORDINARY SIMPLE INTEREST                                                                                     Problem # 11.1:                                                          (a) Find the exact and ordinary simple interest on $8,000 for 50 days   at 10%.                                                                                                                                        'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC4P4       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 12: EXACT INTEREST, ORDINARY INTEREST, EXACT TIME,APPROXIMATE    TIME                                                                                                                                           Problem # 12.1: Find the exact and ordinary interest on $100,000 at 12%  from January 15th, 1992 to October 1st, 1992 using                      (a) exact time and                                                      (b) ordinary time.                                                                                                                             'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC4P6       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═════════════════╕                                                     │ SIMPLE DISCOUNT └────────────────────────────────────────────────────                                                                         5.00       Simple Discount.                                             ────────────────────────────────────────────────────────────────────────                                                                                 One may interpret the present value of a sum which is due on a          later date as a discounted value of that sum.  SIMPLE DISCOUNT          and SIMPLE INTEREST are two different, but equivalent, ways to          view the present value with respect to the final or accumulated         value of the sum.  When the final value is important, then the          concept and use of the SIMPLE DISCOUNT is appropriate.  On the          other hand, when the present value is important, then the               concept and use of the SIMPLE INTEREST is appropriate.                                                                                        ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 13: SIMPLE DISCOUNT AT AN INTEREST RATE (TRUE DISCOUNT) AND AT   A DISCOUNT RATE (BANK DISCOUNT OR INTEREST IN ADVANCE)                                                                                         Problem # 13.1:                                                          (a) Find the present value at 12% simple interest on $3,000 due in 9    months (270 days). What is the discount?                                (b) Find the simple discount on debt of $3,000 due in 9 months at a     discount rate of 12%. What is the present value?                                                                                               'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC5P1       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 14: DISCOUNTING PROMISSORY NOTES                                                                                                        Problem # 14.1:                                                          (a) Find the proceeds of the sale 10 months (300 days) before the due   date of Mr. John Smith's $6,000 note at a simple interest rate of 8%    for 12 months (360 days), if a 16% discount is applied by Mrs. R. B.    Jones.                                                                                                                                         'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC5P3       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒══════════════════╕                                                    │ PARTIAL PAYMENTS └───────────────────────────────────────────────────                                                                         6.00       Partial Payments.                                            ────────────────────────────────────────────────────────────────────────                                                                                 Financial obligations are very often discharged by a series of          partial payments over the life of the obligation rather than by         a single payment on the due date.  INSTALLMENT BUYING is an             example.  The customer makes a down payment and agrees to make          a stipulated number of weekly or monthly partial payments.  The         total charged interest is usually called "the carrying charge".         In partial payments, the problem is usually to find the sum             required on the due date.  Methods, such as the Residuary or            Merchant's Formula, have been derived to calculate the partial          payments.                                                                                                                                     ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 15: PARTIAL PAYMENTS, INSTALLMENT BUYING, MERCHANT'S (MF),       CONSTANT RATIO (CRF), SERIES OF PAYMENT'S (SPF), DIRECT RATIO (DRF)                                                                            Problem # 15.1: Mr. Craznik buys a personal computer listed at $1,349.   95 cash. He can buy it for $149.95 down and 10 monthly installments of  $130.00 each. Find rates of interest charged using                      (a) Merchant's Formula,                                                 (b) Constant Ratio Formula,                                             (c) Series-of-down-payments Formula, and                                (d) Direct Ratio formula?.                                                                                                                     'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINCPPI2      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════════════╕                                                   │ COMPOUND INTEREST └───────────────────────────────────────────────────                                                                        7.00      Compound Interest.                                            ────────────────────────────────────────────────────────────────────────                                                                                 At stated periods of time, the interest due on a principal can          be paid and the principal which earns the interest remains              unchanged.  Such interest is called "simple".  When the earned          interest is added to the principal at stated intervals, the             interest is said to be COMPOUNDed or converted to principal.            Both the principal and compounded interested grow periodically.         The difference between the compounded amount and the original           principal is called the COMPOUND INTEREST.  A graphical                 comparison of a principal that grows with both simple and               compounded daily interest is shown below:  Notice that the              principal usually grows fastest with some sort of compounding.                                                                                                                                                21-     Principal vs. time                                             d  |     Initial principal=$10                                         d   |     Simple interest rate=10%                                    d     |     Daily compounding                                        d        |                                                           d         18-                                                         d             |                                                     d                 |                                                   d                g  |                                               d                g      |         Principal with daily --------->     d            g          16-         compounding                     d            g                |                                      d         g                      |                                   d        g                          |                               d      g                                |                           d      g  <-------- Principal with        13-                       d    g                  simple interest         |                   d   g                       (no compounding)        |              d   g                                                    |          * g                                                          |     *  *                                                            10-** <----- Initial Principal -----------------------------------------  ||--------------|--------------|--------------|--------------|--------   0             1.1            2.2            3.2            4.3                                    time  (in years)                                                                                                            The equation templates for compounded interest calculations             follow.                                                                                                                                       ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 16: COMPOUND INTEREST, FREQUENCY OF CONVERSION, INTEREST PERIOD, COMPOUND AMOUNT, NOMINAL AND EFFECTIVE RATES                                                                                                   Problem # 16.1:                                                          (a) Find the simple interest on $1,000 for 3 years at 5% simple         interest.                                                               (b) Find the compound interest on $1,000 for 3 years if interest at 5%  is converted annually to principal.                                                                                                            'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC7P1       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 17: APPROXIMATION of INTEREST RATES, COMPOUND INTEREST                                                                                  Problem # 17.1:                                                          (a) At what nominal rate ANNRATE% compounded semiannually will $1000    grow to $2150 in 15 1/2 years?                                          (b) At what nominal rate ANNRATE% compounded quarterly will $125        result in an accumulated value of $190 in a period of 5 years?                                                                                 'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC7P9       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 18: APPROXIMATION of TIME, COMPOUND INTEREST                                                                                            Problem # 18.1:                                                          (a) In what time NUMYEARS will $4000 amount to $8000 if compounded      daily at 8% simple annual interest?                                                                                                            'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC7P13      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════════╕                                                       │ PRESENT VALUE └──────────────────────────────────────────────────────                                                                         8.00      Compound Interest, Present Value, Equation of Value.          ────────────────────────────────────────────────────────────────────────                                                                                 The present value of an amount due in "n" interest periods, is          the sum which, if invested today at a given interest rate,              would yield the amount after "n" interest periods.                                                                                            ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 19: COMPOUND INTEREST, PRESENT VALUE                                                                                                    Discussion: $4,000 is due in 10 years at 8% compounded semiannually,     what is the present value?                                                                                                                     'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC8P1       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 20: COMPOUND INTEREST, PRESENT VALUE                                                                                                    Problem # 20.1:                                                          (a) Find the present value of $6000 due in 5 years and 10 months, if    money is worth 18% compounded daily?                                                                                                           'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC8P4       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒════════════════════╕                                                  │ ORDINARY ANNUITIES └─────────────────────────────────────────────────                                                                         9.00      Ordinary Annuities Certain                                    ────────────────────────────────────────────────────────────────────────                                                                                 An annuity is a series of equal payments made at equal payment          intervals.  When the payments begin and end on specific dates,          the annuity is called "certain".  When payments are made at the         ends of the intervals, the annuity is termed "ordinary".                                                                                      ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                                                                                                       Topic # 21: ORDINARY ANNUITIES CERTAIN,AMOUNT and PRESENT VALUE vs       PAYMENT                                                                                                                                        Problem # 21.1:                                                          (a) Find the amount and present value of an ordinary annuity of $5000   every 6 months for 16 years, 6 months if money is worth 7.5%            compounded semiannually.                                                                                                                       'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC9P2       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 22: ORDINARY ANNUITIES CERTAIN, PERIODIC PAYMENT vs AMOUNT                                                                              Problem # 22.1:                                                          (a) What equal quarterly deposits in a savings account paying 7%        annual interest compounded quarterly will amount to $50,000 in 10       years just after the last deposit?                                                                                                             'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC10P2      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 23: ORDINARY ANNUITIES CERTAIN, FINDING TERM, vs PRESENT VALUE                                                                          Problem # 23.1:                                                          (a) Mr. Zellmann borrows $7750 agreeing to repay the principal and      interest at 6% compounded semiannually by making semiannual payments    of $446 each, the first one due in 6 months. How many payments must he  make?                                                                   (b) For how many years is he under obligation?                                                                                                 'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC10P4      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 24: ORDINARY ANNUITIES CERTAIN, FINDING TERM vs FINAL AMOUNT                                                                            Problem # 24.1:                                                          (a) The XYZ fund of $1M is to be accumulated by union taxes of $50K     every 3 months. If funds earn 7% compounded quarterly (every 3 months), find the number of $50K deposits required.                              (b) Increase the payment to round-down-to-whole-number the number of    deposits.                                                                                                                                      'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC10P6      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 25: ORDINARY ANNUITIES CERTAIN, INTEREST RATE vs PERIODIC        PAYMENT                                                                                                                                        Problem # 25.1:                                                          (a) A camcorder can be bought for $649.50 cash or for $49.50 down and   $45.00 per month for 18 months. What nominal rate compounded monthly    is being charged?                                                       (b) What effective (annual) rate is being charged?                                                                                                                                                                     'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC10P7      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════════╕                                                       │ SINKING FUNDS └───────────────────────────────────────────────────────                                                                        10.0     Amortization and Sinking Funds                                 ────────────────────────────────────────────────────────────────────────                                                                               ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 26: AMORTIZATION, CONSTRUCTING AMORTIZATION SCHEDULE                                                                                    Problem # 26.1:                                                          (a) Construct an amortization schedule for the 4 periodic payments (2   year term) required to amortize a $5000 loan at 10% annual interest,    compounded semiannually, if the first payment is due in 6 months.                                                                              'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC11P2      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 27: AMORTIZATION, SELLER'S EQUITY, BUYER'S EQUITY                                                                                       Problem # 27.1:                                                          (a) Mr. Nurlmann buys a house for $128,000. He puts $25,600 (20%) down  and borrows the balance at 14.75% compounded monthly. He makes equal    payments at the end of each month for the next 30 years. What is his    equity just after making the 50th payment?                                                                                                     'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC11P4      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 28: AMORTIZATION, EXTINCTION OF BONDED DEBTS, DISCHARGE DEBT                                                                            Problem # 28.1:                                                          (a) Construct an extinction schedule for the 3 annual payments          required to discharge $30,000 in the form of $100 bonds bearing 8%      interest.                                                                                                                                      'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC11P5      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 29: AMORTIZATION, INTEREST-BEARING SINKING FUND METHOD,          DISCHARGE DEBT                                                                                                                                 Problem # 29.1:                                                          (a) A debt of $10000 with interest at 5% compounded semiann. is to be   discharged by the sinking fund method. If 8 equal semiann. deposits     are made into the sinking fund which pays 3% comp. semiann. (a) Find    the size of the deposit and                                             (b) the semiannual cost of the debt.                                                                                                                                                                                   'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC11P7      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 30: AMORTIZATION, INTEREST-BEARING SINKING FUND SCHEDULE                                                                                Problem # 30.1:                                                          (a) Calculate a sinking fund schedule for the amortization of a $5000   debt bearing 5 % annual interest if the 4 annual deposits are made      into the fund which pays 3%, the first due in 1 year.                                                                                          'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC11P8      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 31: DEPRECIATION, SINKING FUND METHOD, BOOK AND SCRAP VALUE                                                                             Problem # 31.1:                                                          (a) A personal computer costing $4000 new is estimated to have a        useful life of 3 years and a scrap value of $400. Use the sinking fund  method to find the annual fund deposit at 7%.                           (b) Prepare a depreciation schedule.                                                                                                           'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC11P9      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 32: DEPLETION, SINKING FUND METHOD, PURCHASE PRICE AND SCRAP     VALUE                                                                                                                                          Problem # 32.1:                                                          (a) A small oil well is estimated to yield a net return of $50,000 for  the next 20 years. At the end of this time, the property is assumed to  be worthless. If the replacement sinking fund earns 6% annually, find   the purchase price to yield a return of 8%.                                                                                                    'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1110      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                                                                                         ╒═══════╕                                                               │ BONDS └───────────────────────────────────────────────────────────────                                                                        11.0      Bonds                                                         ────────────────────────────────────────────────────────────────────────                                                                                 A bond is a written contract to pay a fixed sum or redemption           value on a future date known as the redemption date and                 periodic interest payments until the redemption date.  To               completely describe a bond, four items must be specified:  1)           its denomination or face value which is usually a multiple of           $100, 2) its interest rate and payment interval.  For example           7% payable in January and July or "7%, JJ"., 3) its redemption          date which is usually an interest payment date and 4) its               redemption value.  "At par" means that the redemption value and         face value are the same.  Otherwise the redemption value is             expressed as a percentage of the face value.  For example a             $1000 bond redeemable at $1010 is given as a "$1000 bond                redeemable at 101".                                                                                                                           ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 33: BOND, PURCHASE PRICE, BUYING at PREMIUM or DISCOUNT                                                                                 Problem # 33.1:                                                          (a) Is a $500,4 %, JAJO bond redeemable in 25 years at 102 with an      investor's rate of 5% bought at a premium or discount?                  (b) Is a $1,000, 4%, MS bond redeemable in 25 years at par with an      investor's rate of 3% bought at a premium or discount?                                                                                                                                                                 'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1204      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 34: BOND, BOOK VALUE, INVESTMENT SCHEDULE                                                                                               Problem # 34.1:                                                          (a) Construct an investment schedule for a $1,000, 7%, JJ bond          redeemable at par in 2 yrs which is bought to yield 8% compounded       semiannually.                                                                                                                                  'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1205      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 35: BOND, PURCHASE PRICE, BOUGHT BETWEEN INTEREST DATES                                                                                 Problem # 35.1:                                                          (a) A $1,000, 7.5%, JJ bond redeemable at 105 on Jan. 1, 2015 is        bought on Sept. 20, 1992 to yield 9% compounded semiannually. Find the  purchase price.                                                         (b) What is the accrued interest from July 1, 1992?                                                                                                                                                                    'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1206      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 36: BOND, PURCHASE PRICE, BOUGHT BETWEEN INTEREST DATES,EXACT    TIME                                                                                                                                           Problem # 36.1:                                                          (a) A $5,000, 6.5%, MS bond redeemable at 105 on Mar. 1, 2005 is        bought on Oct. 10, 1982 to yield 19% compounded semiannually. Find the  purchase price.                                                         (b) What is the accrued interest from Sept. 1, 1982?                                                                                                                                                                   'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC12A6      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 37: BOND, PURCHASE PRICE, QUOTED PRICE, FLAT PRICE, YIELD RATE                                                                          Problem # 37.1:                                                          (a) A $1,000, 7.5%, JJ bond redeemable at 105 on Jan. 1, 2015 is        bought on Sept. 20, 1992 at a quoted price of 95+3/4 ($957.50). Find    the yield rate.                                                         (b) What is the flat price?                                                                                                                                                                                            'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1207      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 38: BOND, PURCHASE PRICE, QUOTED PRICE, FLAT PRICE, YIELD RATE                                                                          Problem # 38.1:                                                          (a) A $5,000, 6.5%, MS bond redeemable at 105 on Mar. 1, 2005 is        bought on Oct. 10, 1982 at quoted price of 45+1/2 ($2475). Find the     yield.                                                                                                                                         'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC12A7      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 39: BOND, PURCHASE PRICE on INTEREST DATE, YIELD RATE                                                                                   Problem # 39.1:                                                          (a) A $10,000, 12%, JJ bond redeemable at 110 ($11,000) on July 1,      2017 is quoted on Jan. 1, 1992 at 125 ($12,500). What is the yield      rate if purchased on that date?                                                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1208      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 40: BOND, CALLABLE, OPTIONAL REDEMPTION DATES                                                                                           Problem # 40.1:                                                          (a) A $1,000, 7.5%, JJ bond redeemable at 105 on Jan. 1, 2015, but      callable on Jan. 1, 2000, is bought on Sept. 20, 1992 to yield 9%       compounded semiann. Find the purchase price, and book value on Sept.    20, 1992.                                                                                                                                      'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1211      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 41: BOND, ANNUITY, PURCHASE PRICE, BUYING at PREMIUM or DISCOUNT                                                                        Problem # 41.1:                                                          (a) A 20-year annuity bond for $100,000 with interest at 8% compounded  semiannually, is to be paid off in 40 equal semiannual installments,    the first payment due in 6 months. Find an investor's purchase price    at the end of the 5th year to earn 12% compounded semiannually.                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1212      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 42: SERIAL BOND ISSUE,PURCHASE PRICE,BUYING at PREMIUM or        DISCOUNT                                                                                                                                       Problem # 42.1:                                                          (a) A serial bond issue of $200,000 with interest at 14% compounded     semiannually is to be redeemed by payments of $50,000 in 10 yrs., $50,  000 in 12 yrs., and $100,000 in 15 yrs. Find the purchase price of the  issue to yield 6% compounded semiannually. .                                                                                                   'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1213      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════════╕                                                       │ ANNUITIES DUE └───────────────────────────────────────────────────────                                                                        12.0     Annuities Due, Deferred Annuities, Perpetuities                ────────────────────────────────────────────────────────────────────────                                                                                 An annuity due is an annuity with a periodic payment at the             beginning of the payment interval.  The term of the annuity due         runs from the first payment to one payment period after the             last payment.  Otherwise, calculations for annuities due are            similar to those for ordinary annuities certain.                                                                                              ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 43: ORDINARY ANNUITY DUE, AMOUNT, PRESENT VALUE vs PAYMENT                                                                              Problem # 43.1: On the 15th of each month, Mr. Butts deposits $500 into  a bond mutual fund paying 6% compounded monthly.                        (a) How much is in the fund just before the 10th deposit (year          =10/12)?                                                                                                                                       'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1302      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 44: ORDINARY DEFERRED ANNUITY, AMOUNT and PRESENT VALUE vs       PAYMENT                                                                                                                                        Problem # 44.1:                                                          (a) A newly built tractor shed will need repairs at the end of 5 years  when $900 will be required for painting. After that, $900 will be       needed each year for 20 years. Find the present value of the upkeep     fund if money is worth 7.5%.                                                                                                                   'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1303      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 45: PERPETUITY                                                                                                                          Problem # 45.1: The ABC Company is expected to pay a dividend of $1.21   every quarter (1 every 3 months).                                       (a) What should an investor pay for the stock if money is worth 7.5%    compounded quarterly?                                                   (b) 7% compounded daily (1/30 mo)? and                                  (c) 8% effective (12 mo)?                                                                                                                      'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1304      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 46: CAPITALIZED COST, PERPETUITY                                                                                                        Problem # 46.1: A fax machine costs $1500 and lasts 5 years at which     time it has a scrap value of $50. If its replacement costs $2250 and    money is worht 8%,                                                      (a) find the capitalized cost of the fax machine.                                                                                              'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1307      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════════════╕                                                   │ ANNUITIES CERTAIN └───────────────────────────────────────────────────                                                                        13.0     Annuities Certain, General Case                                ────────────────────────────────────────────────────────────────────────                                                                                 An annuity in which the interest period and the payment                 interval do not coincide is called a general annuity.                                                                                         ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 47: GENERAL ANNUITIES CERTAIN, NEW PAYMENT, COMBINING FACTOR                                                                            Problem # 47.1:                                                          (a) If interest is at 7% compounded semiannually, replace payments of   $100 at the end of each month by equivalent payments (INTPAYMN) at the  end of 6 months.                                                                                                                               'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1402      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 48: GENERAL ANNUITIES CERTAIN, AMOUNT and PRESENT VALUE                                                                                 Problem # 48.1:                                                          (a) Find the amount and present value of an annuity of $45,000 a year   for 20 years with interest at 7% compounded semiannually.                                                                                      'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1403      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 49: GENERAL ANNUITIES CERTAIN, AMOUNT and PRESENT VALUE                                                                                 Problem # 49.1:                                                          (a) Find the amount and present value of an annuity of $11,250 a        quarter for 20 years with interest at 7% compounded semiannually.                                                                              'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1404      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 50: GENERAL ANNUITIES CERTAIN, PERIODIC PAYMENT and PRESENT      VALUE                                                                                                                                          Problem # 50.1:                                                          (a) If money is worth 15% effective (annually), what equal payments     PERPAYMN made each month for 30 years will amortize a debt of $100,     000?                                                                                                                                           'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1406      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 51: GENERAL ANNUITIES CERTAIN, PERIODIC PAYMENT AND AMOUNT                                                                              Problem # 51.1:                                                          (a) A certain company wishes to have $1,000,000 in a fund at the end    of 10 years. What deposit PERPAYMN must be made annually if funds pay   7% semiannually?                                                                                                                               'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1407      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 52: GENERAL ANNUITIES CERTAIN, NUMBER PERIODS, TERM and AMOUNT                                                                          Problem # 52.1:                                                          (a) Approximately how many annual deposits of $1000 are needed to       accumulate $150,000 if funds earn 7% compounded quarterly?              (b) What periodic payment will result in an exact number of periodic    payments?                                                                                                                                      'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1408      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 53: GENERAL ANNUITIES CERTAIN, RATE of INTEREST, PRESENT VALUE                                                                          Problem # 53.1:                                                          (a) The Money Supermarket advertises loans of $500 to be repaid in 18   monthly installments of $30 each. Find the effective rate charged.                                                                             'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1409      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒════════════╕                                                          │ MORTALITY  └─────────────────────────────────────────────────────────                                                                         14.0     Probability and the Mortality Table.                           ────────────────────────────────────────────────────────────────────────                                                                                 Mortality data are often used in financial calculations that            require premiums such as for life insurance which are based on          the probability of living and dying.  Shown below is a plot of          the odds of reaching the NEXTAGE based on the current AGE of 50         years.                                                                                                                                                                                                        99-a a                                                                    |      a  a                      Plot of % odds of                      |            a a                 reaching NEXTAGE from                  |                 a  a           current age of 50 years.               |                      a         Based on Mortality data.             81-                          a                                            |                             a                                         |                                 a                                     |                                   a                                   |                                       a                             61-                                         a                             |                                             a                         |                                               a                       |                                                  a                    |                                                     a               42-                                                       a               |                                                           a           |                                                             a         |                                                               a       |                                                                   a 24-                                                                    a  ||--------------|--------------|--------------|--------------|--------  50             56             63             70             76                             ODDS2IT%[a]  vs. NEXTAGE                                                                                                            From the above plot, one can see that one ODDS of living drop           off quickly.  Knowledge of such probability allows estimates of         such things as premiums for life insurance.  If 100                     individuals, now aged 50, were to buy 30 year life insurance            policies of $1000 face value, then, statistically speaking, 76          would be dead (and collect) at age 80.  Thus, to break even, a          pool of something like 76 x $1000 or $76,000 must be built up           through premiums and investments over this period in order to           break even, statistically.                                                                                                                      The mortality data is statistical data.  There is no equation           that can generate it.  It must be collected.  However, once             known, it can be accurately represented in a closed                     mathematical form over a specific age range by a polynomial.            The Program AstroDataFitter 3 was used to calculate an accurate         polynomial regression and generate the equation used to                 "predict" odds of survival versus age.  The next problem makes          use of this equation and also explains how to plot the graph of         odds vs.  next age, shown above.                                                                                                              ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 54: STATISTICS: PROBABILITY and MORTALITY                                                                                               Problem # 54.1:                                                          (a) What are the odds (probability) of an individual who is now 50      years old reaching 65 years old (retirement age) in a any group of 100  people.                                                                 (b) Plot the probability versus the next age.                           .                                                                                                                                              'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINCODDS      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                        ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 55: MATHEMATICAL PROBABILITY                                                                                                            Problem # 55.1: You are playing blackjack (21) alone and you have an     ace (worth 11). Drawing 1 card from a 51-card deck of ordinary playing  cards,                                                                  (a) what is the mathematical probability of getting 21 (an ace with a   10 or face card)?                                                       (b) What is the mathematical probability of getting another ace?        (c) What is the minimum you should charge as a premium for a $100       prize to pick that ace?                                                                                                                        'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1501      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 56: STATISTICAL PROBABILITY                                                                                                             Problem # 56.1: The stock market has been observed to open down on       Mondays for 8 of the 12 trading days over a 3 month period.             (a) What is the statistical probability that the stock market will      open down on Monday?                                                                                                                           'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1502      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 57: STATISTICAL PROBABILITY, EXPECTATION                                                                                                Problem # 57.1: From studies of graduation records at ACME Tech, it was  found that over the last 30 years, the probability that an accepted     veteran student will graduate 4 years later is 0.12. The government     has promised Mr. Souza, a veteran, a $10,000 bonus upon his graduation  4 years from today.                                                     (a) If money is worth 7%, find the value of his $10,000 expectation     today.                                                                                                                                         'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1503      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 58: PROBABILITY and MORTALITY                                                                                                           Problem # 58.1:                                                          (a) Find the probability that a person aged 30 will live for at least   1 year.                                                                 (b) Find the probability that a person aged 30 will live to be 65       years old?                                                              (c) Find the probability that a person aged 65 will die before age 70   and the number of people in a 100 person group of 65 year-olds that     will be dead by age 70.                                                                                                                        'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1505      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 59: PURE ENDOWMENT, STATISTICAL PROBABILITY                                                                                             Problem # 59.1: Mrs. Murphy wants to establish a pure endowment of $1,   000,000 for her daughter Melanie now age 9 payable if and when she      attains the age of 65.                                                  (a) If money is worth 7% effective, find the present value.                                                                                    'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1508      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒════════════════╕                                                      │ LIFE ANNUITIES └─────────────────────────────────────────────────────                                                                         15.0     Life Annuities                                                 ────────────────────────────────────────────────────────────────────────                                                                                 A life annuity is an annuity whose payments continue for all or         for some portion of the life of a particular individual called          the annuitant.  A whole life annuity is one in which the                payments continue as long as the annuitant is alive.  If                payments to the individual are to be made at the end of each            period (month, quarter, or year), the annuity is called an              ordinary whole life annuity or a whole life annuity immediate.          If the payments are to be made at the beginning of the period,          the annuity is called a whole life annuity due.                                                                                               ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 60: ORDINARY WHOLE LIFE ANNUITY                                                                                                         Problem # 60.1:                                                          (a) Find the net single premium NETSINGP for an ordinary whole life     annuity of $10,000 per year for an individual now aged 30 if money is   worth 7% effective.                                                                                                                            'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1601      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 61: WHOLE LIFE ANNUITY DUE                                                                                                              Problem # 61.1:                                                          (a) Find the net single premium NETSINGP for an whole life annuity due  of $10,000 per year for an individual now aged 30 if money is worth 7%  effective.                                                                                                                                     'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1602      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 62: ORDINARY WHOLE LIFE ANNUITY DEFERRED                                                                                                Problem # 62.1:                                                          (a) Find the net single premium NETSINGP for an ordinary whole life     annuity of $10,000 per year with the first payment to begin at age 55   for an individual now aged 30 if money is worth 7% effective.                                                                                  'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINC1603      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                                                                                         16.0     Useful Calculations for Problem Solving in Finance.                                                                                           ║ To automatically load these equations, type Q when the ║              ║ highlight bar appears on the screen.  Scroll down, if  ║              ║ necessary, to light it.                                ║                                                                               Topic # 63: Identifying ARITHMETIC or GEOMETRIC PROGRESSION                                                                                     Problem # 63.1:                                                          (a) Three consecutive terms of a progression are: 3, 6 and 12. Is this  a geometric or arithmetic progression?                                  (b) Do three consecutive numbers: -16, -12, -8 form a progression?                                                                                                                                                     'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE FINCIDAG      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                                                                                         ╒════════════╕                                                          │  GLOSSARY  └──────────────────────────────────────────────────────────                                                                        17.0     Glossary of Terms                                              ────────────────────────────────────────────────────────────────────────                                                                               ║ Note, Use the Jump command to locate a glossary reference.    ║       ║ Scroll the screen until the reference is in the middle at line║       ║ 12.  The Jump box will light up.  Type J to locate.  Repeat   ║       ║ typing A, as needed, to continue the search.                  ║                                                                        Arithmetic progression.  See FINC3P1.                                                                                                         Deferred annuity for retirement.  See FINCDEFA.                                                                                               Geometric Progression.  See FINC3P4.                                                                                                          Negative amortization.  See FINCNEG2.                                                                                                         Refinancing Home Mortgage.  See FINCREF2.                                                                                                     Zero Coupon Bonds.  See FINCZER2.                                                                                                             ╒═════════╕                                                             │ LICENSE └─────────────────────────────────────────────────────────────                                                                        18.0           Product License and Warranty.                            ────────────────────────────────────────────────────────────────────────                                                                                       Software License Agreement  (Registered Users)                                                                                            If you are a registered user, PCSCC grants you the right to use         this Software for a single-user computer or a workstation not           attached to a network.  You may not rent or lease this Software         without the expressed written permission of PCSCC.  You may not         decompile, disassemble, reverse engineer, copy, create a                derivative work, or otherwise use this Software except as               stated in this agreement.  The license authorizes you to create         and use an extra copy of the Software on a home or laptop               computer, as long as the extra copy is never loaded at the same         time this Software is loaded on the primary computer on which           you use this Software.                                                                                                                          If any provision of this agreement is found to be unlawful,             void, or unenforceable, then that provision shall be severed            from this Agreement and will not affect the validity and                enforceability of any of the remaining provisions.  This                agreement shall be governed by the laws of the State of                 Delaware.                                                                                                                                       The Software and accompanying materials are provided with               Restricted Rights.  Use, duplication, or disclosure by the              Government is subject to restrictions as set forth in                   subparagraph (c) (1) (ii) of The Rights in Technical Data and           Computer Software clause at DFARS 252.227-7013, or                      subparagraphs (c) (1) and (2) of the Commercial Computer                Software--Restricted Rights at 48 CFR 52.227-19, as applicable.         Contractor/manufacturer is PC SuperComputer Capital,                    Incorporated, at the address listed below.                                                                                                      Non registered users must comply with the Shareware policy              described elsewhere in this software Pacakage.                                                                                                  Type T to return to the Table of Contents.                                                                                                                       Warranty Information                                                                                                           PC SuperComputer Capital, Inc.  (PCSCC) hereby disclaims all            warranties relating to this Software, whether express or                implied, including without limitation any implied warranties of         merchantability or fitness for a particular purpose.  PCSCC             will not be liable for any special, incidental, consequential,          indirect or similar damages due to loss of data, loss of                profits, lost savings or any other reason, even if PCSCC or an          agent of PCSCC has been advised of the possibility of such              damages.  In no event shall PCSCC's liability for any damages           ever exceed the price paid for the license to use Software,             regardless of the form of the claim.  The person using the              Software bears all risk as to the quality and performance of            the Software.  This Software is licensed AS IS.                                                                                                 Any action or proceeding brought by either party against the            other arising out of or related to this agreement shall be              brought in a STATE or FEDERAL COURT of competent jurisdiction           located in Fairfield County, Connecticut.  The parties hereby           consent to in personam jurisdiction of said courts.                                                                                             Type T to return to the Table of Contents.                                                                                             ╒══════════════╕                                                        │ USER SUPPORT └────────────────────────────────────────────────────────                                                                        19.0              User Support.                                         ────────────────────────────────────────────────────────────────────────                                                                                 This program has undergone over 5 years of "beta testing"               around the world.  The algorithms have been in use since 1976,          are proven and believed highly reliable.  However,                      comprehensive programs of this nature may develop what are              called "bugs".  User support is provided to all registered              users for a minimum of 3 months without charge.  Registered             users can receive such help via phone/mail.  Registration also          enrolls the user for notification of "bug" fixes, upgrades, new         versions, new products and many more benefits.  For the phone           number/mail address see below or position the jump line here            and type J.  ∙Registration∙.  Support will be provided to             non-registered users and users beyond the free support period           on a time and materials basis.                                                                                                         ╒═══════════════╕                                                       │ PRODUCT  INFO └───────────────────────────────────────────────────────                                                                        20.0       Product Information and How to Order Complete Package.       ────────────────────────────────────────────────────────────────────────                                                                                 AstroFormulaCalculator 3 Product Description 7-1-1993                                                                                           AstroFormulaCalculator 3 is a unique and innovative mathematics         tool which offers productivity enhancements not found in any            other software package either retail or shareware.  This                hands-on program combines the functions of both a spreadsheet           and calculator; but it is better.  Why?  Because it is right            between the two:  Easier than a spreadsheet and more powerful           than a calculator.  With its special format-free interface,             formula or equation-based iterations are much easier to set up          than in a spreadsheet.  It is designed to be "smarter" which            makes it very user-friendly for Professionals of all levels,            especially for the infrequent or "computer-shy" user.  Broad            applications exist in many disciplines where calculations with          formulas, equations or other math recipes are required such as          in Economics, Genetics, Chemistry, Electrical Engineering,              Engineering Mechanics, Fluid Mechanics & Hydraulics, Finance,           Physics, Statistics and even Nursing.  Features include:                                                                                        ∙ DOS or Windows as non-Windows application.  Runs on all PC            compatibles.  DOS 2.1+, Monochrome display, 200K RAM, floppy or         disk.                                                                                                                                           ∙ DOS command line support for any direct calculation such as           addition, multiplication, subtraction and division.                                                                                             ∙ Format-free entry of up to 63 equations with at least 256             independent variables and 256 constants.  Smart and                     "hassle-free" interpreter.                                                                                                                      ∙ Equations and formulas are written according to the BASIC             conventions.  Versatile library of built-in functions.                                                                                          ∙ Advanced calculator functions including many automated                numerical methods such as:                                                                                                                      ∙ Newton-Raphson for solving x in y=f(x)                                ∙ Advanced simplex for solving x at W=Y=Z in W=f(x), Y=g(x),              Z=h(x)                                                                ∙ Numerical integration (two methods)                                   ∙ Numerical differentiation                                             ∙ Summation                                                             ∙ Finding maxima and minima                                             ∙ Plotting equations                                                    ∙ Saving/retrieving data files with full file management                  support                                                               ∙ Screen dumps as DOS text files for inclusion in documents                                                                                     ∙ Highly-structured documentation, on-line with Table of                Contents, Glossary and search function.  Interactive with               program.                                                                                                                                        ∙ On-line helpfile.  Comprehensive summary of                             commands/functions with step-by-step examples on uses of all            advanced functions.                                                   ∙ On-line user manual.  A "learn by example" document which               illustrates the universal nature of problem-solving with many           step-by-step examples from Science, Engineering and Finance.                                                                                  ∙ Full support for ACTION21 and ACTION11 data sets.                                                                                             ∙ Comments from users:                                                                                                                   ∙ "... calculate circuit board drilling and routing speeds...easy to       use, versatile and powerful with good documentation."                                                                    J. L.  New York     ∙ "...used the integration capability to determine defect density...do     not have any tool (either PC or host based) that does for me what       ...(AstroFormCalc 3)...does."                                                                                            J. R.  Virginia     ∙ "...for Electrical Engineering practice it is better than a              spreadsheet and a calculator..."                                                                                         C. B.  Florida      ∙ "...used to do frequency spectrum work and calculations on circuits,     ...of real value and a productivity tool."                                                                               E. S.  California   ∙ "...one of a handful of scarcely available packages...in the types       of numeric problems they solve."                                                                                         W. C.  Chile                                                                                       This productivity-enhancing tool has been developed by the team         at PC SuperComputer Capital, Inc.  Order the complete version           of AstroFormulaCalculator 3 today!                                                                                                     ╒════════════════╕                                                      │ OTHER PRODUCTS └──────────────────────────────────────────────────────                                                                        21.0              Software Included in Astro 3 Registration             ────────────────────────────────────────────────────────────────────────                                                                                 Register for AstroFormulaCalculator 3 and receive, in addition          to the most recent version of ACAL3.EXE and ACAL3HLP.HLP, these         3 powerful math analysis programs:  AstroEquationSolver 3,              AstroDataFitter 3 and AstroShadowBox 3.  Each has its own               extensive and interactive on-line helpfile written just like            the one your reading now.  A print program is included which            prints theses helpfiles to the standard printer or to a DOS             text file.  All Astro 3 programs are written with the same              high-level user-friendly front-end requiring minimal effort to          setup and execute relatively elaborate calculations.  All data          sets and helpfiles are compatible among members of the family.          A brief summary of the other members of the Astro 3 shareware           family included with the registration package follows:                                                                                    ∙ AstroEquationSolver 3 - Solves both linear and nonlinear                    simultaneous equations with up to 30 unknowns.  Characterized           by extremely easy setup.  Uses active/inactive method of                AstroFormulaCalculator 3 to select variables.  Strictly high            level.  No reference to matrices at all!.  Includes program             ASOL3.EXE and extensive on-line help file ASOL3HLP.HLP that             includes many learn-and-use examples.                                                                                                     ∙ AstroDataFitter 3 - Fit data to any algebraic expression.                   Nonlinear optimization.  Fully-automated polynomial regression          with automatic "equation generator".  Easy to use, even by a            novice.  Will generate interpolated tables from fitted                  equations.  Up to 30 "active" variables.  Up to 500 data                points.  "Smart" algorithm requires minimal user input to solve         problems.  DOS text plots of "fit".  Point-by-point listing of          fitted data.  Residual variance, correlation coefficient,               coefficient of determination and much more!  Includes program           AFIT3.EXE and extensive on-line help file AFIT3HLP.HLP that             includes many illustrated examples.                                                                                                       ∙ AstroShadowBox 3 - The pop-up resident member (TSR) of the                  Astro 3 team.  Provides math support for other DOS programs.            Pop-up via hot key, surround calculation in "shadow box", and           type "(enter)" to pass result down through keyboard buffer or           pop up, enter calculation and pass result down.  Great for              adding powerful and interactive math capabilities to DOS text           editors such as Brief (tm, Borland), PE2 (tm, IBM) or                   WordPerfect (tm, WordPerfect).  Extensive features also include         screen dumps with appends as DOS text files or as parsed                columns in 123 (tm, Lotus) .WK1 files.  Requires as little as           15K of main memory.  Includes program ABOX3.EXE and on-line             help file ABOX3HLP.HLP                                                                                                                          If you like Engineering, Science or Finance and you have ideas          that you could transform into an interactive helpfile like              SCIFIN.HLP (The Astro 3 Science Manual) or PHYCAL.HLP ( The             Astro 3 Physics Manual) or FINCAL.HLP (The Astro 3 Finance              Manual), then you should write one and market it!  If you write         it in a commercial spreadsheet format, you will not likely be           able to distribute a fully functional package which is the mark         of a true Shareware program and the policy of the Association           of Shareware Professionals!  However, the AstroUtility 3                program provides the tools needed to generate an Astro 3                interactive application file with a minimum of effort AND               REGISTERED USERS OF THE AstroUtility 3 PROGRAM RECEIVE A LIMTED         DISTRIBUTION LICENSE WHICH ALLOWS INCLUSION OF ANY OR ALL OF            THE ASTRO 3 PROGRAMS IN YOUR PACKAGE!                                                                                                     ∙  AstroUtility 3  -   Support for authors to construct their own             on-line application help files.  Develop equation files in your         favorite editor and translate them into .EQU format for final           "test and touch-up".  Likewise, develop an application file in          your favorite editor, automatically include information from            previously developed .EQU files, and then compile a                     full-feature .HLP with automatic Table of Contents, line                numbers and so on.  .HLP files support all apostrophe commands          and many other useful features such as CalcMerge with lets you          dynamically stuff values calculated in the main equation                display into the application file.  As with the other Astro 3           programs, AstroUtility 3 comes with its own interactive and             extensive on-line help file which can be printed, if needed.            Application files can contain up to 64,000 lines!                                                                                               See below for instructions on ∙Registration∙.                                                                                          ╒══════════════╕                                                        │ REGISTRATION └───────────────────────────────────────────────────────                                                                         22.0                 Order/Registration Form                            ────────────────────────────────────────────────────────────────────────                                                                                 If a printer is available, position the order form (part 1) on          the screen and type the "(print screen)" key to make a copy.            Then, advance the text and position the order form (part 2) on          the screen and type "(print screen)" again to finish.                                                                                                  ASTRO 3 Products Order/Registration Form  (part 1)                                                                                  Name:________________________________  Title:________________                                                                                   Company:_____________________________________________________                                                                                   Address:____________________________ City:___________________                                                                                   State:___________   Zip:_____________  Country:______________                                                                                   Date:_____/_____/_____           (Fill out form completely)                                                                                     ---------------------------------------------------------------         Product                     #     Price/ea     S&H       Total          ---------------------------------------------------------------         AstroFormulaCalculator 3   ___    _$29.95_    _$5.00_   _______         Complete Package includes                                               ACAL3, ASOL3, AFIT3 + ABOX3                                                                                                                     AstroUtility 3 + ASTRO3    ___    _$99.95_    _$5.00_   _______         distribution license                                                ------------------------------------------------------------------------------------------------------------------------------------------------                ASTRO3 Products Order/Registration Form  (part 2)                                                                                   * Canadian Orders, Add $2.00 per copy                   _______                                                                                 * International Orders, Add $6.00 per copy              _______                                                                                 * CT Residents add appropriate sales tax                _______                                                                                                                  TOTAL ENCLOSED      __________                                                                                 Disk Size: [ ] 5-1/4"   [ ] 3-1/2"   [ ] Check  [ ] Visa  [ ] MC                                                                                Card# __________________________________     Exp. Date ________                                                                                 Signature ______________________________                                                                                                        How did you hear about our Products?    [ ] BBS   [ ] Friend            [ ] Other _____________________________________________________                                                                                               Mail Completed form with Payment to:                                                                                                                  PCSCC, Inc.   Dept. AC3H                                                   P. O. Box 173                                                        Botsford,  CT   06404  USA                                                                                                  Support ONLY,  1-203-270-9079     E-mail to CIS, 72263,1657                                                                                          [Mar 1994]  Prices subject to change without notice.                                                                                                  Type T to return to the Table of Contents.                                                                                       ╒═════════════════════╕                                                 │ MANUAL INSTALLATION └─────────────────────────────────────────────────                                                                        23.0         Instructions for Manually Installing Package.              ────────────────────────────────────────────────────────────────────────                                                                             The following are minimal instructions for manually installing                                 AstroFormulaCalculator 3.                                                                                           ∙ Minimum distribution files:  README.1ST, ACAL3.ICO, ACAL3.EXE,          ACAL3HLP.HLP, FINCAL.HLP and *.EQU.                                                                                                           ∙ These files will probably be bundled in a compressed file such as       FINCAL.ZIP, FINCAL.LHZ, or something similar.  Please unload.                                                                                 ∙ Create a DOS directory named ASTRO3 and change to it:                   cd\ (enter)    md\astro3 (enter)  cd \astro3 (enter)                                                                                          ∙ Copy ACAL3.EXE, ACAL3HLP.HLP, ACAL3.ICO and FINCAL.HLP and *EQU         into the directory ASTRO3                                                                                                                     ∙ Add these statements to AUTOEXEC.BAT in the base directory:             SET ASTRO3=C:\ASTRO3                                                    append to existing PATH statement  ;C:\ASTRO3;                                                                                                ∙ Running Under Windows as a Non-Windows Application                                                                                             Follow the installation instructions and install on the hard drive C.   Start WINDOWS (tm, MicroSoft).  Click on FILE then click on PROPERTIES. Enter the following information for each of the fields.  Description:   AstroFormCalc 3, Command:  ACAL3.EXE, Working Directory:  \ASTRO3.      Click on CHANGE ICON.  Enter Filename:  C:\astro3\acal3.ico.  Click on  OK to exit and click on OK to exit FILE.  The AstroFormCalc 3 icon      should appear in the accessory window.  Click on it to run ACAL3.                                                                              ∙ To start from DOS:  cd\astro3 (enter)  then  FINCAL (enter)             or:                 acal3 \astro3\fincal.hlp (enter)                                                                                          ∙ To start with the on-line help file, type                                                   cd\astro3 (enter) then acal3 ? (enter)                                                                                    ╒═════════════╕                                                         │ AUTHOR ???? └─────────────────────────────────────────────────────────                                                                        24.0           Interested in Becoming the Author of Your Own                         Interactive Application File?                              ────────────────────────────────────────────────────────────────────────                                                                                 Many technologies are based on math/algebra.                            AstroFormulaCalculator 3 and its interactive, problem-solving           application files offer distinct advantages to the Author.  The         *.EQU templates are easy to develop and PCSCC offers complete           support for compiling these into the interactive application            files such as the help file ACAL3HLP.HLP or SCIFIN.HLP (The             Astro 3 Science Manual) or PHYCAL.HLP (The Astro 3 Physics              Manual) or FINCAL.HLP (The Astro 3 Finance Manual).                     Application files can be written for any level of user from the         very beginner to the Ph.D.  and distributed with any or all of          the ASTRO 3 family of programs.  See the OTHER PRODUCTS               section above for more details.  To automatically jump type "J"         if the jump bar is highlighted on those words.                                                                                         ╒═══════════╕                                                           │ HELP FILE └───────────────────────────────────────────────────────────                                                                        25.0       Help File: Summary of File Viewing Commands                  ────────────────────────────────────────────────────────────────────────                                                                            A - Auto-search of entire text for user-supplied string. Search is          in uppercase and is case insensitive. If string found,                  type A to continue or to enter new string, type (space) A.          B,N - Move back or ahead 18 lines.  Also use (backspace) for "B".       E, (esc) - Exit from help file to equations display.                    F,T,K - Jump to the first (beginning), T.O.C or last (end) line.        G - Skip to Glossary of terms or summary of functions, if present.      J,(ent) - Search line on │JUMP│, Reference is after . Jump to                    line number or perform autosearch ahead if text reference.    L,P - Jump to line/page. Type Lxxx(ent) or Pyy(ent) to jump to                line #xxx or page #yy. With + or -, ahead or back 56 lines.       S,R - Skip ahead (S) or back (R) in help file to major headings         W - Skip to Summary of useful calculations or warnings, if present      1 to 9 - Typing 1 to 9 advances the text by 1 to 9 lines.               (ctrl Q) - Exit from help file.  Same as command "E".                   Edit keys - Use edit keys: (Home) (up arrow) (PgUp) (left arrow)                    (right arrow) (End) (down arrow) (PgDn).                                                                                             Entry into the application file is at/near the last position.           Type: T to return to Table of Contents or E to exit the file.      