Introduction to Finance

annual percentage rate (APR) 
determined by multiplying the 
interest rate charged per period by 
the number of periods in a year
eff ective annual rate (EAR) 
measures the true interest rate 
when compounding occurs more 
frequently than once a year
3
Some fi nancial calculators are preprogrammed with an “interest rate conversion” function, with which one can easily 
switch between an EAR (sometimes called EFF% for the “eff ective” rate) and the APR.

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C H A PT E R 9 Time Value of Money
Compounding interest quarterly means that the bank is paying interest four times a year 
to its depositors. Option 1 involved four periods per year and a periodic interest rate, 
r
, of 
8 percent divided by 4, or 2 percent. Every dollar invested under option 1 will grow to $1.0824 
[$1(1 + 0.02)
4
] after one year’s time. Another way of expressing this is that the eff ective 
annual rate of 8 percent compounded quarterly is 8.24 percent.
Under option 2, the relevant time period is one month and the periodic interest rate is 
8 percent ÷ 12, or 0.67 percent. Every dollar invested under option 2 will grow to $1.0830 [$1(1 + 
0.0067)
12
]. Thus, the eff ective annual rate of 8 percent compounded monthly is 8.30 percent.
As option 2 gives the depositor more interest over the course of a year, depositors should 
choose it over option 1. This example illustrates that, for the same APR or stated rate, more 
frequent compounding increases the future value of an investor’s funds more quickly.
LEARNING ACTIVITY
Go to the Board of Governors of the Federal Reserve website, http://www.federalreserve.
gov. Access “Consumer Information” and describe some of the types of “consumer help” 
provided by the Federal Reserve. 
Applying Finance To...