Copyright © 2008, The McGraw-Hill Companies, Inc.
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CHAPTER 3
SUMMARY
Topic Key Ideas, Formulas, and Techniques Example(s)
The Concept of Compound
Interest, pp. 86–88
- Simple interest is only paid on the original
principal, not on accumulated interest - Compound interest is paid both on principal
and on accumulated interest
See discussion at the
beginning of Chapter 3.1.
Calculating Future Value with
Compound Interest, p. 93
- The compound interest formula: FV PV(1 i)n
- Substitute present value, interest rate per
period, and number of time periods into the
formula - Be careful to follow order of operations when
evaluating the formula
Suppose you invest
$14,075 at 7.5% annually
compounded interest. How
much will this grow to in
20 years? (Example 3.1.2)
Calculating Compound
Interest, p. 93
- Find the future value, using the compound
interest formula - The amount of compound interest is the
difference between the PV and the FV
Suppose you invest $14,075
at 7.5% annually compounded
interest. How much interest
will you earn over 20 years?
(Example 3.1.3)
Calculating Present Value
with Compound Interest, p. 94
- Substitute future value, interest rate per period,
and number of time periods into the compound
interest formula - Use the principle of balance to solve for PV
How much money should I
invest today into an account
paying 7^3 / 8 % annually
compounded interest to have
$2,000 fi ve years from now.
(Example 3.1.5)
The Rule of 72, p. 96 • The doubling time for money growing at x%
compound interest is approximately 72/x
- The compound interest rate required to double a
sum of money in x years is approximately 72/x%
What compound interest
rate is required for $30,000
to grow to $1,000,000 in
30 years? (Example 3.1.8)
Compounding Frequencies,
p. 103
- If interest compounds more frequently than
once a year, the same compound interest
formula is used - i must be the interest rate per period. The
annual rate must be divided by the number of
time periods per year - n must be the number of time periods. The term
in years must be multiplied by the number of
time periods per year.
Find the future value of
$3,250 at 4.75% interest
compounded daily for
4 years. (Example 3.2.2)
Comparing Compounding
Frequencies, pp. 104–105
- The more frequently a given interest rate
compounds, the more interest.
Compare the future value
of $5,000 in 5 years at 8%
compounded annually,
semiannually, quarterly,
monthly, biweekly, and daily.
(Example 3.2.5)
Continuous Compounding
(Optional), p. 106
- Continuous compounding assumes that interest
compounds “infi nitely many” times per year - The continuous compounding formula: FV PV ert
- e is a mathematical constant, approximately
2.71827 - Continuous compounding only provides slightly
more interest than daily compounding
Find the future value of
$5,000 at 8% for 5 years
assuming continuous
compounding. (Example
3.2.7)
(Continued)