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			12.4	%
					Monthly			13.3
					Weekly			11.0
					Infinite			14.7

Answer 1

EAR=(1+APR/m)^m-1
where m=compounding periods

1.

0.124=(1+APR/2)^2-1

(1+0.124)^(1/2)=1+APR/2

Hence APR=[(1+0.124)^(1/2)-1]*2

=12.04%(Approx).

2.

0.133=(1+APR/12)^12-1

APR=[(1+0.133)^(1/12)-1])*12

=12.55%(Approx).

3.

0.11=(1+APR/52)^52-1

APR=[(1+0.11)^(1/52)-1]*52

=10.45%(Approx)

4.

EAR=e^APR-1

where e=2.71828

0.147=2.71828^APR-1

1.147=2.71828^APR

Taking log on both sides;

log 1.147=APR*log 2.71828

APR=log 1.147/log 2.71828

which is equal to

=13.71%(Approx).