{"text_format":"3","workbook":"xls","n_sheets":7,"sheets":["PV Factor","Amortization","PV ","Functions","Monthly compounding","Car Loan","Mortgage"],"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"PV Factor","index":0,"n_rows":19,"n_cols":5,"rows_kept":19,"flags":["formulas_cached_only"]}
["FUTURE AND PRESENT VALUE FACTORS"]
[]
[]
["Interest rate",null,{"v":0.1,"d":"10%"}]
["Present value",null,{"v":1000,"d":"1,000"}]
[]
[null,"First of",null,"End of","% of "]
[null,"Year",null,"Year","Initial"]
["Year","Balance","Interest","Balance","Investment"]
[]
[1,{"v":1000,"d":"1,000"},100,{"v":1100,"d":"1,100"},{"v":1.1,"d":"110%"}]
[2,{"v":1100,"d":"1,100"},110,{"v":1210,"d":"1,210"},{"v":1.21,"d":"121%"}]
[3,{"v":1210,"d":"1,210"},121,{"v":1331,"d":"1,331"},{"v":1.331,"d":"133%"}]
[4,{"v":1331,"d":"1,331"},{"v":133.1,"d":"133"},{"v":1464.1,"d":"1,464"},{"v":1.4641,"d":"146%"}]
[]
[]
["% of Initial Investment ( Future Value Factor )  =  ( 1 + Interest Rate ) ^ # of Years"]
[]
["Present Value Factor  = 1 / ( 1 + Interest Rate ) ^ # of Years"]

{"sheet":"Amortization","index":1,"n_rows":19,"n_cols":5,"rows_kept":19,"flags":["formulas_cached_only"]}
["AMORTIZATON TABLE"]
[]
[]
["The following amortization table shows the link between the present value (amount "]
["borrowed), cash flow (payment) and discount rate (interest rate) on a five-year loan."]
[]
[]
["Interest rate",{"v":0.1,"d":"10%"}]
["Payment",{"v":1000,"d":"1,000"}]
["Amount borrowed",{"v":3790.7867694084507,"d":"3,791"}]
[]
[null,"Beginning","Plus","Less","Ending"]
["Year","Balance","Interest","Payment","Balance"]
[]
[1,{"v":3790.7867694084507,"d":"3,791"},{"v":379.07867694084507,"d":"379"},{"v":-1000,"d":"(1,000)"},{"v":3169.865446349296,"d":"3,170"}]
[2,{"v":3169.865446349296,"d":"3,170"},{"v":316.9865446349296,"d":"317"},{"v":-1000,"d":"(1,000)"},{"v":2486.8519909842253,"d":"2,487"}]
[3,{"v":2486.8519909842253,"d":"2,487"},{"v":248.68519909842254,"d":"249"},{"v":-1000,"d":"(1,000)"},{"v":1735.5371900826476,"d":"1,736"}]
[4,{"v":1735.5371900826476,"d":"1,736"},{"v":173.55371900826478,"d":"174"},{"v":-1000,"d":"(1,000)"},{"v":909.0909090909124,"d":"909"}]
[5,{"v":909.0909090909124,"d":"909"},{"v":90.90909090909125,"d":"91"},{"v":-1000,"d":"(1,000)"},{"v":3.637978807091713e-12,"d":"0"}]

{"sheet":"PV ","index":2,"n_rows":15,"n_cols":7,"rows_kept":15,"flags":["formulas_cached_only"]}
["PRESENT VALUE CALCULATION"]
[]
[]
["The following shows how to calculate the present value as the sum of the present values"]
["of the cash flows."]
[]
["Interest rate",{"v":0.1,"d":"10%"}]
["Payment",{"v":1000,"d":"1,000"}]
[]
["Year",0,1,2,3,4,5]
[]
["Payment",null,{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"}]
["Present value factor",{"v":1,"d":"100%"},{"v":0.9090909090909091,"d":"91%"},{"v":0.8264462809917354,"d":"83%"},{"v":0.7513148009015777,"d":"75%"},{"v":0.6830134553650705,"d":"68%"},{"v":0.6209213230591549,"d":"62%"}]
["PV of payment",null,{"v":909.090909090909,"d":"909"},{"v":826.4462809917354,"d":"826"},{"v":751.3148009015777,"d":"751"},{"v":683.0134553650705,"d":"683"},{"v":620.9213230591549,"d":"621"}]
["PV of all payments",{"v":3790.7867694084475,"d":"3,791"}]

{"sheet":"Functions","index":3,"n_rows":35,"n_cols":7,"rows_kept":35,"flags":["formulas_cached_only"]}
["SPREADSHEET FUNCTIONS"]
[]
["Given the number of periods (or number of payments), any two of the following determine "]
["the third:  present value, cash flow, discount rate.  Be careful about the signs!"]
[]
["1. The present value is computed as PV(interest rate, # of periods, cash flow)."]
[]
["Discount rate",{"v":0.1,"d":"10%"}]
["Number of periods",5]
["Cash flow",{"v":1000,"d":"1,000"}]
["Present value",{"v":-3790.7867694084507,"d":"(3,791)"}]
[]
[]
["2. The present value can also be computed as NPV(interest rate, series of cash flows)."]
[]
["Year",0,1,2,3,4,5]
[]
["Cash flow",null,{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"}]
["PV of cash flows",{"v":3790.786769408447,"d":"3,791"}]
[]
[]
["3. The cash flow is computed as PMT(discount rate, # of periods, present value)."]
[]
["Discount rate",null,{"v":0.1,"d":"10%"}]
["Number of periods",null,5]
["Present value",null,3791]
["Cash flow",null,{"v":-1000.0562496928791,"d":"(1,000)"}]
[]
[]
["4. The discount rate is computed as IRR(series of present value and cash flows)."]
[]
["Year",0,1,2,3,4,5]
[]
["Cash flow",{"v":-3790.7867694084507,"d":"(3,791)"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"},{"v":1000,"d":"1,000"}]
["Internal rate of return",{"v":0.10000000000000223,"d":"10%"}]

{"sheet":"Monthly compounding","index":4,"n_rows":25,"n_cols":5,"rows_kept":25,"flags":["formulas_cached_only"]}
["MONTHLY COMPOUNDING"]
[]
["Annual interest rate",null,{"v":0.1,"d":"10%"}]
["Monthly interest rate",null,{"v":0.008333333333333333,"d":"0.83%"},null," ( Annual rate / 12 )"]
[]
[{"$nulls":4},"Future"]
[null,"Beginning",null,"Ending","Value"]
["Month","Balance","Interest","Balance","Factor"]
[]
[1,{"v":100,"d":"100.00"},{"v":0.8333333333333334,"d":"0.83"},{"v":100.83333333333333,"d":"100.83"},{"v":1.0083333333333333,"d":"100.83%"}]
[2,{"v":100.83333333333333,"d":"100.83"},{"v":0.8402777777777778,"d":"0.84"},{"v":101.6736111111111,"d":"101.67"},{"v":1.016736111111111,"d":"101.67%"}]
[3,{"v":101.6736111111111,"d":"101.67"},{"v":0.8472800925925926,"d":"0.85"},{"v":102.5208912037037,"d":"102.52"},{"v":1.025208912037037,"d":"102.52%"}]
[4,{"v":102.5208912037037,"d":"102.52"},{"v":0.8543407600308642,"d":"0.85"},{"v":103.37523196373456,"d":"103.38"},{"v":1.0337523196373455,"d":"103.38%"}]
[5,{"v":103.37523196373456,"d":"103.38"},{"v":0.8614602663644547,"d":"0.86"},{"v":104.23669223009902,"d":"104.24"},{"v":1.04236692230099,"d":"104.24%"}]
[6,{"v":104.23669223009902,"d":"104.24"},{"v":0.8686391019174918,"d":"0.87"},{"v":105.10533133201652,"d":"105.11"},{"v":1.0510533133201647,"d":"105.11%"}]
[7,{"v":105.10533133201652,"d":"105.11"},{"v":0.8758777611001377,"d":"0.88"},{"v":105.98120909311666,"d":"105.98"},{"v":1.0598120909311661,"d":"105.98%"}]
[8,{"v":105.98120909311666,"d":"105.98"},{"v":0.883176742442639,"d":"0.88"},{"v":106.8643858355593,"d":"106.86"},{"v":1.0686438583555924,"d":"106.86%"}]
[9,{"v":106.8643858355593,"d":"106.86"},{"v":0.8905365486296609,"d":"0.89"},{"v":107.75492238418896,"d":"107.75"},{"v":1.077549223841889,"d":"107.75%"}]
[10,{"v":107.75492238418896,"d":"107.75"},{"v":0.897957686534908,"d":"0.90"},{"v":108.65288007072387,"d":"108.65"},{"v":1.086528800707238,"d":"108.65%"}]
[11,{"v":108.65288007072387,"d":"108.65"},{"v":0.9054406672560322,"d":"0.91"},{"v":109.5583207379799,"d":"109.56"},{"v":1.0955832073797982,"d":"109.56%"}]
[12,{"v":109.5583207379799,"d":"109.56"},{"v":0.9129860061498326,"d":"0.91"},{"v":110.47130674412973,"d":"110.47"},{"v":1.1047130674412964,"d":"110.47%"}]
[]
["Effective annual rate",null,{"v":0.10471306744129638,"d":"10.47%"}]
[]
["Effective annual rate  =  FVF - 100%  =  ( 1 + Monthly Rate )^12 - 100%"]

{"sheet":"Car Loan","index":5,"n_rows":371,"n_cols":5,"rows_kept":371,"flags":["formulas_cached_only"]}
["Principal",{"v":15000,"d":"$15,000"}]
["Interest rate",{"v":0.08,"d":"8.00%"}]
["Number of years",4]
["Monthly payment",{"v":366.1938351225398,"d":"$366.19"}]
[]
["If the principal or interest rate are changed, the monthly payment and the following "]
["amortization table will automatically recalculate."]
[]
[null,"Beginning","Plus","Less","Ending"]
["Month","Balance","Interest","Payment","Balance"]
[]
[1,{"v":15000,"d":"15,000.00"},{"v":100,"d":"100.00"},{"v":-366.1938351225398,"d":"(366.19)"},{"v":14733.80616487746,"d":"14,733.81"}]
[2,{"v":14733.80616487746,"d":"14,733.81"},{"v":98.2253744325164,"d":"98.23"},{"v":-366.1938351225398,"d":"(366.19)"},{"v":14465.837704187437,"d":"14,465.84"}]
[3,{"v":14465.837704187437,"d":"14,465.84"},{"v":96.43891802791626,"d":"96.44"},{"v":-366.1938351225398,"d":"(366.19)"},{"v":14196.082787092813,"d":"14,196.08"}]
[4,{"v":14196.082787092813,"d":"14,196.08"},{"v":94.6405519139521,"d":"94.64"},{"v":-366.1938351225398,"d":"(366.19)"},{"v":13924.529503884225,"d":"13,924.53"}]
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[12,{"v":11972.285046920804,"d":"11,972.29"},{"v":79.8152336461387,"d":"79.82"},{"v":-366.1938351225398,"d":"(366.19)"},{"v":11685.906445444403,"d":"11,685.91"}]
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[21,{"v":9325.06685943808,"d":"9,325.07"},{"v":62.16711239625388,"d":"62.17"},{"v":-366.1938351225398,"d":"(366.19)"},{"v":9021.040136711794,"d":"9,021.04"}]
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{"$rows_empty":102}
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{"sheet":"Mortgage","index":6,"n_rows":371,"n_cols":5,"rows_kept":371,"flags":["formulas_cached_only"]}
["Principal",{"v":150000,"d":"$150,000"}]
["Interest rate",{"v":0.085,"d":"8.50%"}]
["Number of years",30]
["Monthly payment",{"v":1153.3702253764998,"d":"$1,153.37"}]
[]
["If the principal or interest rate are changed, the monthly payment and the following "]
["amortization table will automatically recalculate."]
[]
[null,"Beginning","Plus","Less","Ending"]
["Month","Principal","Interest","Payment","Principal"]
[]
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