Question

Find the APR, or stated rate, in each of the following cases (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.):

Stated Rate (APR)	Number of Times Compounded	Effective Rate (EAR)
%	Semiannually	10.50%
	Monthly	11.4
	Weekly	9.1
	Infinite	12.8

  

Answer 1

EAR=(1+APR/m)^m-1

where m=compounding periods

1.

0.105=(1+APR/2)^2-1

(0.105+1)^(1/2)=1+APR/2

Hence

APR=[(0.105+1)^(1/2)-1]*2

=10.24%

2.

0.114=(1+APR/12)^12-1

Hence

APR=[(1+0.114)^(1/12)-1]*12

which is equal to

=10.84%(Approx).

3.

0.091=(1+APR/52)^52-1

Hence

APR=[(1+0.091)^(1/52)-1]*52

which is equal to

=8.72%(Approx)

4.

EAR=(e^APR)-1

where e=2.71828

0.128=(2.71828^APR)-1

(1+0.128)=2.71828^APR

Taking log on both sides;

log 1.128=APR*log 2.71828

Hence APR=log 1.128/log 2.71828

which is equal to

=12.04%(Approx).