The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

135

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)