Question

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

Standard rate (APR) %	Number of times Compounded	Effective Rate (EAR)
	semiannually	11.3%
	Monthly	12.2%
	Weekly	9.9%
	Infinite	13.6%

Answer 1

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

0.113=(1+APR/2)^2-1

(1+0.113)=(1+APR/2)^2

(1.113)^(1/2)=(1+APR/2)

APR=[(1.113)^(1/2)-1]*2

=11%(Approx).

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

0.122=(1+APR/12)^12-1

(1+0.122)=(1+APR/12)^12

(1.122)^(1/12)=(1+APR/12)

APR=[(1.122)^(1/12)-1]*12

=11.57%(Approx).

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

0.099=(1+APR/52)^52-1

(1+0.099)=(1+APR/52)^52

(1.099)^(1/52)=(1+APR/52)

APR=[(1.099)^(1/52)-1]*52

=9.45%(Approx).

4.EAR=(e)^APR-1
where e=2.71828

0.136=(2.71828)^APR-1

(1+0.136)=(2.71828)^APR

1.136=(2.71828)^APR

Taking log on both sides;

log 1.136=APR*log 2.71828

APR=log 1.136/log 2.71828

=12.75%(Approx).