The Mathematics of Money

FV 
 PV(1  i)n

FV
$1,200  1  0.06_____ 12 

9

FV
$1,200(1.04591058)

FV
$1,255.09

Since the question asked for the amount of interest to be earned, we subtract to get

$1,255.09  $1,200 
 $55.09.

Nonannual Compounding and the Rule of 72

In Section 3.1 we discussed the Rule of 72 when interest compounds annually. Can we

still use this rule if the interest compounds more often? The answer to this question is yes.

While, as we have seen, compounding frequency does make a difference, the difference is

modest, and the Rule of 72 is an approximation anyway. The frequency of the compounding

can thus be ignored when you are using this rule. Compounding frequency makes a differ-

ence, of course, but the difference is not large enough to seriously affect the Rule of 72.

EXERCISES 3.2

A. The Concept of Nonannual Compounding

1. A bank account with an initial balance of $1,450 pays 6% interest compounded quarterly. Using the simple interest
   formula to fi nd the interest earned each quarter, fi ll in the missing values in the following table, showing the growth in
   the account’s value over the fi rst year.

Quarter Beginning Balance Interest Earned

End of Quarter

Balance

1 $1,450.00

2

3

4

B. Using the Compound Interest Formula

2. For each of the following combinations of interest rates, compounding frequencies and terms, fi nd the value of i (the
   interest rate per period) and n (the number of periods) that would be used in the compound interest formula. The value
   of i may be either left as a fraction or divided out to its decimal form.

a. 8%, quarterly compounding, 10 years

b. 9%, compounded monthly, 7 years

c. 15%, compounded semiannually, 15 years

d. 5%, daily compounding using bankers rule, 8 years

3. For each of the following combinations of interest rates, compounding frequencies and terms, fi nd the value of i (the
   interest rate per period) and n (the number of periods) which would be used in the compound interest formula. The
   value of i may be either left as a fraction or divided out to its decimal form.

a. 5%, daily compounding using the simplifi ed exact method, 8 years

b. 7.19%, compounded quarterly, 2 years

c. 3.03%, compounded daily, 1 year

d. 4^3 ⁄ 4 %, compounded monthly, 29 years

110 Chapter 3 Compound Interest