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finance
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Wrap
Microsoft Windows Help File Content
|
1995-05-08
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25KB
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380 lines
R-Tek Scratchpad
Version 1.00
TSPadDatad
TPictured
TCommentTextd
TLogFontd
Times New Roman
densed BT
Financial Problems
nnnnnnnnnnnnnnnnnn]
TCommentTextd
Five Value Problems
nnnnnnnnnnnnnnnnnnn]
TCommentTextd
Five value problems are financial problems involving these five interdependent variables:Y
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
Present Value
nnnnnnnnnnnnn]
TCommentTextd
Future Value
nnnnnnnnnnnn]
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Number of Payment Periods
nnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
Interest per payment period
nnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
the Payment Value itself
nnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
To solve problems of this sort, first create a five element vector and set the four known
elements. Then call the function fiveval(m, n) where m is the 5 vector with the appropriate
4 values set. n is the index of the element that is to be calculated based on the other four.
The function returns a new 5 vector containing the same 4 original elements with the n-th
element set at the solved value.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
Each element of the m vector must contain a particular variable. We will use the following
assignments to make our program easier to read:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
TCommentTextd
Present Value
nnnnnnnnnnnnn]
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Future Value
nnnnnnnnnnnn]
TExpressiond
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Number of Payment Periods
nnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
The value assigned to each of these variables
is its index in the vector mJ
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
nPmts:3
TCommentTextd
Interest per payment period
nnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
intr:4
TExpressiond
pmt:5
TCommentTextd
the Payment Value itself
nnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m:zmat(1,5)
TCommentTextd
Create a 5 vector that initially contains all zeros3
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
Example 1:
nnnnnnnnnn]
TCommentTextd
Calculate a monthly interest payment knowing loan value, the term of the loan,
and the APR (annual percentage rate)t
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[pv]:110000.00
TCommentTextd
Amount of loan
nnnnnnnnnnnnnn]
TExpressiond
m[fv]:0.00
TCommentTextd
Indicates loan is to be completely paid off+
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[nPmts]:15*12
TCommentTextd
15yr loan with monthly payments
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
8.5% APR Divide by 12 to get monthly interest.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[intr]:8.5%/12
TCommentTextd
Use fiveval to calculate unknown and save result
back into the original m vectorP
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m:fiveval(m,pmt)
TExpressiond
m[pmt]
TCommentTextd
Monthly payment determined by other 4 variables/
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
THardPageBreakd
TCommentTextd
Example 2:
nnnnnnnnnn]
TCommentTextd
Calculate how much one can afford to borrow knowing the term of the loan,
the APR, and the maximum monthly payment one can handle.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[fv]:0.00
TCommentTextd
Indicates loan is to be completely paid off+
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[nPmts]:30*12
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30yr loan with monthly payments
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[intr]:8.5%/12
TCommentTextd
8.5% APR Divide by 12 to get monthly interest.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[pmt]:750.00
TCommentTextd
Maximum affordable monthly payment"
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m:fiveval(m,pv)
TCommentTextd
Amount of loan one can afford to borrow'
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[pv]
TCommentTextd
Example 3:
nnnnnnnnnn]
TCommentTextd
Continue on with example 2. Consider that we borrowed the maximum we could
presently afford, but with the intention of making monthly payments for only
5yrs and then paying the loan off in full. Such a payment is called a
balloon payment. The problem is this: What is the balloon payment amount?
We solve this by calculating the balance due on the loan after making the
60th monthly payment. We make our balloon payment at the same time we
make the 60th payment so:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[nPmts]:5*12
TCommentTextd
The other values of m come from the calculation
of fiveval in problem 2G
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m:fiveval(m,fv)
TCommentTextd
Calculate the balance due after 60 payments+
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[pmt]+m[fv]
TCommentTextd
The balloon payment is the final monthly payment
plus the balance due after making the final paymentd
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
Example 4:
nnnnnnnnnn]
TCommentTextd
Calculate the total interest paid over the term of the loan;
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[pv]:100000.00
TCommentTextd
Borrow $100,000
nnnnnnnnnnnnnnn]
TExpressiond
m[fv]:0.00
TCommentTextd
Pay it off
nnnnnnnnnn]
TExpressiond
m[nPmts]:30*12
TCommentTextd
30yr loan
nnnnnnnnn]
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Interest rate
nnnnnnnnnnnnn]
TExpressiond
m[intr]:8.5%/12
TExpressiond
m:fiveval(m,pmt)
TExpressiond
m[pmt]
TCommentTextd
Calculated payment
nnnnnnnnnnnnnnnnnn]
THardPageBreakd
TCommentTextd
There are two functions to calculate the interest and principal for specific payment ranges.\
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
ifiveval(m, p1, p2) calculates the interest paid from payment p1 to payment p2 inclusiveX
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
pfiveval(m, p1, p2) calculates the principal paid from payment p1 to payment p2 inclusiveY
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
So, the total interest on the above loan is:,
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
ifiveval(m,1,m[nPmts])
TCommentTextd
The total paid on the $100,000 mortgage is the amount borrowed plus the interest paid:V
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
total:m[pv]+ifiveval(m,1,m[nPmts])"
TCommentTextd
Alternatively, you can arrive at the total more simply for this case by multiplying the
payment amount by the number of payments:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
total:m[pmt]*m[nPmts]
TCommentTextd
and get the total interest by subtracting the principal:8
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
total-m[pv]
TCommentTextd
ifiveval and pfiveval are most useful for the more complicated cases of determing principal
and interest between interim payments - such as determining the total interest paid on
a house mortgage during a year so that the individual can take the appropriate tax deduction.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
Example 5:
nnnnnnnnnn]
TCommentTextd
Go back up a few lines, change the interest rate to 15%, and rerun. Now take a look
at the total cost of the loan. Frightening, isn't it?!
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
THardPageBreakd
TCommentTextd
Example 6:
nnnnnnnnnn]
TCommentTextd
Examine how rapidly the loan is repaid, but first consider what fraction of each
payment goes to interest(which does not help to repay the loan)
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TGraphd
TGraphSetupDatad
TTraced
TExpressiond
ifiveval(m,n,n)/m[pmt]
TExpressiond
TExpressiond
TExpressiond
m[nPmts]
TCommentTextd
You can easily see that at the beginning, almost the entire payment goes to interest
so you can probably predict the shape of the curve that shows the payoff value of the
loan after each payment period.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TGraphd
TGraphSetupDatad
TTraced
TExpressiond
m[pv]-pfiveval(m,1,n)
TExpressiond
TExpressiond
TExpressiond
m[nPmts]
TCommentTextd
Yet another way of looking at this, consider a graph of total paid, total interest paid
and total principal paidp
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnn]
TGraphd
TGraphSetupDatad
TTraced
TExpressiond
n*m[pmt]
TTraced
TExpressiond
ifiveval(m,1,n)
TTraced
TExpressiond
pfiveval(m,1,n)
TExpressiond
TExpressiond
TExpressiond
m[nPmts]
THardPageBreakd
TCommentTextd
Example 7:
nnnnnnnnnn]
TCommentTextd
You want to open a savings account and deposit the same amount every month
for the next 10 years. What should your deposit be to have a total of $30000
at the end of 10 years assuming an interest rate of 5%? This differs from the
preceding examples in that the first payment is made at the beginning of the
first period. This form of annuity is called "annuity due". The functions
available to handle annuity due calculations have the ordinary name with b (for
beginning) appended. This example calls for the use of such a function, ie
fivevalb(m, n). Another point to note is that the payments calculated for this
kind of problem are negative.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[pv]:0.00
TCommentTextd
start with no money in the account"
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
amount we wish to accumulate
nnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[fv]:30000.00
TExpressiond
m[nPmts]:120
TCommentTextd
10 years
nnnnnnnn]
TCommentTextd
interest rate for deposit
nnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[intr]:5.0%/12
TExpressiond
m:fivevalb(m,pmt)
TCommentTextd
calculated necessary monthly deposit$
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
m[pmt]
TCommentTextd
Other financial functions:
nnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
The APR is the annual percentage rate. It is the interest rate per compounding period
multiplied by the number of compounding periods per year.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TCommentTextd
The EFF is the annual effective rate. It is the interest rate that produces the same interest
as the APR, but with a single annual compounding period.
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnznnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn]
TExpressiond
EFFtoAPR(8.0,12)
TExpressiond
APRtoEFF(8.0,12)
TPrinterDimensionsd
TSPadInitDatad
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Times New Roman
densed BT
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Arial
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Arial
TLogFontd
Symbol
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Symbol
TNumberFormatDatad
TGraphSetupDatad
TPageSetupDatad
151.0
ea1.0
eB1.0
R-Tek Scratchpad Example File FINANCE