a) What is the future value of a 5-year ordinary annuity with annual payments of

Question

a) What is the future value of a 5-year ordinary annuity with annual payments of $309, evaluated at a 7 percent interest rate? (Do not include the dollar sign ($), and round your answer to 2 decimal places: for example, 536.34)

b) You are negotiating to buy a new car with a car salesman at a local dealer. You have negotiated the price to $35,000. You have $3,000 to put towards the down payment and plan to get a loan for the rest. If you can get an annual interest rate of 6 percent APR (with monthly compounding) over a 5-year period, what would be your monthly payment? Round it to 2 decimal place (cents), e.g., 234.56

Explanation / Answer

Solution A

Annual payment = 309

Period = 5 years

R = 7%

Future value of the annuity = $309(FVIFA7%,5) = 309 x 5.751 = 1777.059

Solution B

Monthly payment = {P x R x (1+R)n} / (1+R)n-1

R = (6/12)*100

N = 60 months

P = 35000 – 3000 = 32000

Monthly payment = {32000 x (6/12)*100 x (1+(6/12)*100 )60 / (1+(6/12)*100 )59 = $281.77

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