Fundamentals of Financial Management (Concise 6th Edition)

148 Part 2 Fundamental Concepts in Financial Management

The same logic applies when we! nd present values under semiannual

compounding. Again, we use Equation 5-8 to convert the stated annual rate to the

periodic (semiannual) rate and Equation 5-9 to! nd the number of semiannual pe-

riods. We then use the periodic rate and number of periods in the calculations. For

example, we can! nd the PV of $100 due after 10 years when the stated annual rate

is 5%, with semiannual compounding:

Periodic rate! 5%/2! 2.5% per period

Number of periods! 10(2)! 20 periods

PV of $100! $100/(1.025)^20! $61.03

We would get this same result with a! nancial calculator:

N I/YR PV PMT FV

20 2.5 0 –100

61.03

If we increased the number of compounding periods from 2 (semiannual) to 12

(monthly), the PV would decline to $60.72; and if we went to daily compounding,

the PV would fall to $60.66.

5-16 COMPARING INTEREST RATES

Different compounding periods are used for different types of investments. For

example, bank accounts generally pay interest daily; most bonds pay interest

semiannually; stocks pay dividends quarterly; and mortgages, auto loans, and

other instruments require monthly payments.^10 If we are to compare investments

or loans with different compounding periods properly, we need to put them on a

common basis. Here are some terms you need to understand:

• The nominal interest rate (INOM), also called the annual percentage rate (APR)
  (or quoted or stated rate), is the rate that credit card companies, student loan
  of! cers, auto dealers, and so forth, tell you they are charging on loans. Note
  that if two banks offer loans with a stated rate of 8% but one requires monthly
  payments and the other quarterly payments, they are not charging the same
  “true” rate—the one that requires monthly payments is charging more than

Nominal (Quoted, or

Stated) Interest

Rate, INOM

The contracted (or quoted

or stated) interest rate.

Nominal (Quoted, or

Stated) Interest

Rate, INOM

The contracted (or quoted

or stated) interest rate.

Annual Percentage

Rate (APR)

The periodic rate times the

number of periods per

year.

Annual Percentage

Rate (APR)

The periodic rate times the

number of periods per

year.

SEL

F^ TEST Would you rather invest in an account that pays 7% with annual compound-

ing or 7% with monthly compounding? Would you rather borrow at 7% and

make annual or monthly payments? Why?

What’s the future value of $100 after 3 years if the appropriate interest rate is

8% compounded annually? compounded monthly? ($125.97; $127.02)

What’s the present value of $100 due in 3 years if the appropriate interest rate

is 8% compounded annually? compounded monthly? ($79.38; $78.73)

(^10) Some banks even pay interest compounded continuously. Continuous compounding is discussed in Web
Appendix 5A.