130 Part 2 Fundamental Concepts in Financial Management
5-2e Graphic View of the Compounding Process
Figure 5-1 shows how a $1 investment grows over time at different interest rates.
We made the curves by solving Equation 5-1 with different values for N and I. The
interest rate is a growth rate: If a sum is deposited and earns 5% interest per year,
the funds on deposit will grow by 5% per year. Note also that time value concepts
can be applied to anything that grows—sales, population, earnings per share, or
future salary.Future Value of $10 1 2 3 4 5 6 7 8 9 101.002.003.004.005.006.00I = 0%I = 5%I = 10%I = 20%PeriodsGrowth of $1 at Various Interest Rates and Time Periods
F I G U R E 5! 1Explain why this statement is true: A dollar in hand today is worth more than
a dollar to be received next year.
What is compounding? What’s the di# erence between simple interest and
compound interest? What would the future value of $100 be after 5 years at
10% compound interest? at 10% simple interest? ($161.05; $150.00)
Suppose you currently have $2,000 and plan to purchase a 3-year certi! cate
of deposit (CD) that pays 4% interest compounded annually. How much will
you have when the CD matures? How would your answer change if the inter-
est rate were 5% or 6% or 20%? ($2,249.73; $2,315.25; $2,382.03;
$3,456.00) (Hint: With a calculator, enter N = 3, I/YR = 4, PV = #2000, and
PMT = 0; then press FV to get 2,249.73. Enter I/YR = 5 to override the 4%
and press FV again to get the second answer. In general, you can change
one input at a time to see how the output changes.)
A company’s sales in 2008 were $100 million. If sales grow at 8%, what will
they be 10 years later, in 2018? ($215.89 million)
How much would $1, growing at 5% per year, be worth after 100 years? What
would FV be if the growth rate was 10%? ($131.50; $13,780.61)SELF^ TEST