A. Compound Interest Formula:FV = P (1 + r) nFuture Value = FV, P = Principal, r = interest rate and n = number of years.
= $500(1 + 0.06) 10a) An initial $500 compounded for 10 years at 6 percent.
A = $ 895b) An initial $500 compounded for 10 years at 12 percent.
500(1 + 0.12) 10B = $1553Present Value Calculation:PV = present Value, Principal = $ 500, r = interest rate and n = number of yearsFormula:PV = FV/(1 + r) nThe present value of $500 due in 10 years at a 6 percent discount rate.
PV = $ 500 / (1 + 0.06) 10c) The present value of $500 due in 10 years at a 6 percent discount rate.
C = $ 279.20d) The present value of $1,552.90 due in 10 years at a 12 percent discount rate and at a 6 percent rate.
At 6 % = $ 867.13At 12 % = $ 499.99Definition of Present valueThe free dictionary defines Present Value as, The amount of cash today that is equivalent in value to a payment, or to a stream of payments, to be received in the future. To determine the present value, each future cash flow is multiplied by a present value factor. For example, if the opportunity cost of funds is 6%, the present value of $500 to be received in ten year is $ 500 /(1 + 0.06) 10 = $ 279.20 For $ 1552.90 due in 10 years at a 12 percent discount rate and at a 6 percent rate. The present value is $ 867.13 % and $ 499.99 respectively.
B Future Value of an Annuity:The Future Value of an Ordinary Annuity (FVoa) is the value that a stream of expected or promised future payments will grow to after a given number of periods at a specific compounded interest.
Formula:FVoa = PMT [((1 + i)n - 1) / i]FVoa = Future Value of an Ordinary AnnuityPMT = Amount of each paymenti = Interest Rate Per Periodn = Number of Periods2. Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1;that is, they are ordinary annuities (Also note that you can leave values in the TVM register, switch to 'BEG', press, and find the FV of the annuity due.)A) $400 per year for 10 years at 10 percent.
FVoa =? PMT = $ 400 I = 10 % n = 10 yearsCalculation using Excel sheet:Year12345678910Begin040084013241856.42442.043086.2443794.8684574.3555431.791Interest04084132.4185.64244.204308.6244379.4868457.4355543.1791Deposit400400400400400400400400400400End40084013241856.42442.043086.2443794.8684574.3555431.7916374.97FVoa = PMT [((1 + i)n - 1) / i]= 400[((1+0.1) 10 - 1)/0.10]= $ 6374.97B) $200 per year for 5 years at 5 percent.
Year12345Begin0200410630.5862.025Interest01020.531.52543.10125Deposit200200200200200End200410630.5862.0251105.126FVoa = PMT [((1 + i)n - 1) / i]= 200[((1+0.05) 5 - 1)/0.05] = $ 1105.126C) $400 per year for 5 years at 0 percent.
Year12345Begin040080012001600Interest00000Deposit400400400400400End400800120016002000FVoa = PMT [((1 + i)n - 1) / i]= 400[((1+0) 5 - 1)/0] = $ 2000C: Present value for various compounding periods:3. Find the present value of $500 due in the future under each of the following conditions:a) 12 percent nominal rate,...