Question

5) ?(Compound interest with? non-annual periods?) You just received a bonus of ?$5,000.

a. Calculate the future value of ?$5,000?, given that it will be held in the bank for 9 years and earn an annual interest rate of 7 percent. ?(Round to the nearest? cent.)

b. Recalculate part ?(a?) using a compounding period that is? (1) semiannual and? (2) bimonthly.

c. Recalculate parts ?(a?) and ?(b?) using an annual interest rate of 14 percent.

d. Recalculate part ?(a?) using a time horizon of 18 years at an annual interest rate of 7 percent.

e. What conclusions can you draw when you compare the answers in parts ?(c?) and ?(d?) with the answers in parts ?(a?) and ?(b?)?

Answer 1

Amount = $ 5000, Interest = 7% and time = 9 years

a. Future Value = Amount*(1+Interest)^Time = 5000*(1+7%)^9 = $ 9192.30

b.

1. Semiannual

Future Value = 5000*(1+7%/2)^(2*9) = $ 9287.45

2. Bimonthly

Future Value = 5000*(1+7%/6)^(6*9) = $ 9353.88

c. Future Value = Amount*(1+Interest)^Time = 5000*(1+14%)^9 = $ 16259.74

1. Semiannual

Future Value = 5000*(1+14%/2)^(2*9) = $ 16899.66

2. Bimonthly

Future Value = 5000*(1+14%/6)^(6*9) = $ 17373.79

d. Future Value = Amount*(1+Interest)^Time = 5000*(1+7%)^18 = $ 16899.66

1. Semiannual

Future Value = 5000*(1+7%/2)^(2*18) = $ 17251.33

2. Bimonthly

Future Value = 5000*(1+7%/6)^(6*18) = $ 17499.02