## Solutions to Time Value of Money Practice Problems

*Prepared by Pamela Peterson Drake*
- 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.

- 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)

- 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.

- 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).

- 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.