Investments, tenth edition

 Example  5.4 

EAR versus APR 

  Annual Percentage Rates 

 Annualized rates on short-term investments (by convention,  T  , 1 year) often are reported 

using simple rather than compound interest. These are called    annual  percentage  rates,  

or   APRs.    For example, the APR corresponding to a monthly rate such as that charged 

on a credit card is reported as 12 times the monthly rate. More generally, if there are  n  

compounding periods in a year, and the per-period rate is  r  

 f 

   ( T  ), then the APR  5   n   3   r  

 f 

   ( T  ). 

Conversely, you can find the per-period rate from the APR as  r  

 f 

   ( T  )  5   T   3  APR. 

 Using this procedure, the APR of the 6-month bond in Example 5.2 with a 6-month 

rate of 2.71% is 2  3  2.71  5  5.42%. To generalize, note that for short-term investments 

of length  T,  there are  n   5  1/ T  compounding periods in a year. Therefore, the relationship 

among the compounding period, the EAR, and the APR is   

 

1 1 EAR 5

31 1 r

f

(T )

4

n

5

31 1 r

f

(T)

4

1/T

5

31 1 T 3 APR4

1/T

 

 (5.8)   

 Equivalently,   

APR 5

(1 1 EAR)

T

2 1

T