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

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

- 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?

- 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.
- How much must they deposit today in the account in order to
satisfy the estimated tuition?
- 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?

**Solutions to 5-minute Work-out**
- Hint: identify PV, FV, and t
- 9.54%
- 7.79
- 3.71%
- 9.05%

- 36 months or 3 years
- Hint: PV five years from today is $31,913.56
- $25,005.11
- $5,775.58