5-minute Work-out for the Time Value of Money

1. Calculate the average annual interest rate on each of the following transactions:
   1. You borrow $1,000 and repay $1,200 at the end of two years.
   2. You borrow $1,000 and repay $1,350 at the end of four years.
   3. You borrow $500 and repay $600 at the end of five years.
   4. You borrow $250 and repay $500 at the end of eight years.

2. Suppose you want to save $8,000 for a new car. If you deposit $185.71 every month, beginning in one month, in an account that pays 12% interest per year, compounded monthly, how long will you be saving for your car?

3. The Appletons are saving money to send Johnny to college. They estimate that when Johnny enters college six years from today, they should be prepared to pay $9,000 per year for each of the four years, with each year's tuition payable at the beginning of each school year. They expect to earn 5% on the savings.
   1. How much must they deposit today in the account in order to satisfy the estimated tuition?
   2. How much must they deposit each year, beginning one year from today, into the account if they intend to make the last deposit the year prior to Johnny entering college?

1. Hint: identify PV, FV, and t
   1. 9.54%
   2. 7.79
   3. 3.71%
   4. 9.05%
2. 36 months or 3 years
3. Hint: PV five years from today is $31,913.56
   1. $25,005.11
   2. $5,775.58