The Mathematics of Money

(Darren Dugan) #1

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)
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