## Solutions to Time Value of Money Practice Problems

Prepared by Pamela Peterson Drake
1. How long does it take for an investment to quadruple in value if the investment yields 6% per year?
• PV=\$1
• FV=\$4
• r=6%
• n=24 years
• Hint: Use \$1 as a PV; therefore the FV = \$4 if the value quadruples.
2. What is the effective annual rate of interest for a loan that has an 18% annual percentage rate, compounded monthly?
• r=1.5%
• n=12
• EAR=19.56%
• Hint: First translate the rate into a monthly one, and then compound for a year (12 months)
3. The average price of a movie ticket at the end of 1988 was \$5.50 and the average price of a movie ticket at the end of 1990 was \$6.00. At what annual rate did ticket prices grow?
• PV=\$5.50
• FV=\$6.00
• n=2
• r=4.4466%
• Hint: There are two years over which the price has grown, 1989 and 1990.
4. If I invest \$100 today in an account that eans 10% per year, compounded semi-annually, how much will I have in this account at the end of twenty years if I make no withdrawals?
• PV=\$100
• r=10%/2=5%
• n=20x2=40
• FV=\$704
• Hint: translate parameters to a semi-annual basis (i.e., period = six months).
5. Suppose that I am trying to borrow money from you to finance my business. And suppose that I promise to repay you in two installments, one payment in two years of \$5,000 and one payment in four years for \$10,000. If your opportunity cost of funds is 10%, how much are you willing to lend me?
• PV of first payment = \$4,132
• PV of second payment = \$6,830
• Loan = sum of PVs = \$10,962
• Hint: if you have a financial calculator, you can solve this is one step using the cash flow registers (CF0=0, CF1=0, CF2=5000, CF3=0, CF4=10000) and solve for NPV.