Question

1. Calculating Future Values. What is the future value of $3,100 in 17 years assuming an interest rate of 8.4 percent compounded semiannually?
2. Calculating APR. Elliott Credit Corp. wants to earn an effective annual return on its consumer loans of 17.1 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers? Explain why this rate is misleading to an uninformed borrower.
3. Calculating Annuity Cash Flows. If you put up $41,000 today in exchange for a 5.1 percent, 15-year annuity, what will the annual cash flow be?

Answer 1

a)

Semi annual rate = 8.4% / 2 = 4.2%

Number of periods = 17 * 2 = 34

Future value = Present value (1 + rate)^time

Future value = 3100 (1 + 0.042)^34

Future value = 3100 * 4.05044

Future value = $12,556.37

b)

There are 365 days in a year

Effective annual rate = (1 + APR/n)^n - 1

0.171 = (1 + APR/365)^365 - 1

1.171 = (1 + APR/365)^365

1.00043 = 1 + APR/365

0.00043 = APR/365

APR = 0.1579 or 15.79%

APR = Annual percentage rate

Banks are required to report APR. However, APR can be misleading as shown in the calculation. The APR is lower than effective rate. Uninformed borrower will think his/her borrowing rate is 15.79% whereas the actual rate is 17.1%. Uninformed borrower would know how to calculate effective rate.

c)

Present value = Annual cash flow * [1 - 1 / (1 + rate)^time] / rate

41,000 = Annual cash flow * [1 - 1 / (1 + 0.051)^15] / 0.051

41,000 = Annual cash flow * [1 - 0.4742] / 0.051

41,000 = Annual cash flow * 10.30985

Annual cash flow = $3,976.78