Principles of Managerial Finance

CHAPTER 4 Time Value of Money 181

annual percentage rate (APR)
The nominal annual rate of
interest, found by multiplying the
periodic rate by the number of
periods in 1 year, that must be
disclosed to consumers on credit
cards and loans as a result of
“truth-in-lending laws.”

annual percentage yield (APY)
The effective annual rate of
interest that must be disclosed to
consumers by banks on their
savings products as a result of
“truth-in-savings laws.”

11. The effective annual rate for this extreme case can be found by using the following equation:
    EAR (continuous compounding)ek 1 (4.23a)
    For the 8% nominal annual rate (k0.08), substitution into Equation 4.23a results in an effective
    annual rate of
    e0.08 1 1.0833 1 0.08338.33%
    in the case of continuous compounding. This is the highest effective annual rate attainable with an
    8% nominal rate.

EXAMPLE Fred Moreno wishes to find the effective annual rate associated with an 8% nom-

inal annual rate (i0.08) when interest is compounded (1) annually (m1);

(2) semiannually (m2); and (3) quarterly (m4). Substituting these values into

Equation 4.23, we get

1. For annual compounding:

EAR 1  

1

 1 (10.08)^1  1  1 0.08 1 0.088%

2. For semiannual compounding:

EAR 1  

2

 1 (10.04)^2  1 1.0816 1 0.08168.16%

3. For quarterly compounding:

EAR 1  

4

 1 (10.02)^4  1 1.0824 1 0.08248.24%

These values demonstrate two important points: The first is that nominal and

effective annual rates are equivalent for annual compounding. The second is that

the effective annual rate increases with increasing compounding frequency, up to

a limit that occurs with continuous compounding.^11

At the consumer level, “truth-in-lending laws” require disclosure on credit

card and loan agreements of the annual percentage rate (APR).The APR is the

nominal annual rate found by multiplying the periodic rate by the number of

periods in one year. For example, a bank credit card that charges 1^1 / 2 percent per

month (the periodic rate) would have an APR of 18% (1.5% per month 12

months per year).

“Truth-in-savings laws,” on the other hand, require banks to quote the

annual percentage yield (APY)on their savings products. The APY is the effective

annual rate a savings product pays. For example, a savings account that pays 0.5

percent per month would have an APY of 6.17 percent [(1.005)^12 1].

Quoting loan interest rates at their lower nominal annual rate (the APR) and

savings interest rates at the higher effective annual rate (the APY) offers two

advantages: It tends to standardize disclosure to consumers, and it enables finan-

cial institutions to quote the most attractive interest rates: low loan rates and high

savings rates.

0.08



4

0.08



2

0.08



1