- At a town board meeting, the fi nancial manager states that the town’s fi nancial situation has improved. However, while
it is no longer borrowing money to fund its operations, interest on prior borrowings continues to compound, and if
nothing is done the town’s debt will double in the next 10 years. Approximately what interest rate is the town paying on
its debt? At this rate, how long would it take for the debt to quadruple? - Gita plans to open a CD with a goal of having $2,500 in the account after 2 years. If the best rate she can fi nd is 5.97%
compounded annually, how much should she deposit to reach her goal? - Five years ago, Jill deposited $1,172.39 in an account that has consistently paid 4.11% compounded annually. How
much interest has she earned? - Wes put $2,000 into an investment account that pays 7.5% annually compounded interest. Approximately how long
will it take for his deposit to grow to $32,000? Using this period of time, fi nd the future value of $2,000 at 7.5%
compounded annually to see how good your approximation was. - Moshe invested $2,500 at 6% compounded annually for 8 years. How much did he end up with?
- Find the future value of $3,255.09 at 6.17% annually compounded interest for 1 year.
- I invested $1,011.35 in a 6-year CD that pays 7.15% compounded annually. How much more interest will I earn than if
I had invested my money at 7.15% simple interest? - Ryann borrowed $3,031.95 at 9.34% annually compounded interest for 2 years. How much total interest will
she pay? - As of July 26, 2005, the total debt of the U.S. federal government was $7,870,499,539,830, which works out to
$26,534 per person. Assume that the only growth in the debt per person comes from interest on the existing debt, and
not from any changes in the U.S. population or from any additional borrowing.^2 Assuming an interest rate of 4.5%
compounded annually, how much will your share of the debt have grown to in 2035?
F. Additional Exercises
- Oliver and Olivia both opened 4-year CDs on the same day. Oliver deposited $3,500, and his account paid 6.25%
compounded annually. Olivia’s account paid only 5.55% compounded annually, but she ended up with exactly the same
account value as Oliver. How much did Olivia deposit? - I invested $1,011.35 in a 1-year CD that pays 7.15% compounded annually. How much more interest would I earn than
if I had invested my money at 7.15% simple interest? Compare your result to Exercise 31.
(^2) This problem is obviously completely hypothetical.
100 Chapter 3 Compound Interest