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		10.6	%
			Monthly		11.5
			Weekly		9.2
			Infinite		12.9

Answer 1

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

0.106=(1+APR/2)^2-1

(1+0.106)=(1+APR/2)^2

(1.106)^(1/2)=(1+APR/2)

APR=[(1.106)^(1/2)-1]*2

=10.33%(Approx).

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

0.115=(1+APR/12)^12-1

(1+0.115)=(1+APR/12)^12

(1.115)^(1/12)=(1+APR/12)

APR=[(1.115)^(1/12)-1]*12

=10.93%(Approx).

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

0.092=(1+APR/52)^52-1

(1+0.092)=(1+APR/52)^52

(1.092)^(1/52)=(1+APR/52)

APR=[(1.092)^(1/52)-1]*52

=8.81%(Approx).

4.

EAR=(e)^APR-1

where e=2.71828

0.129=(2.71828)^APR-1

1.129=2.71828^APR

Taking log on both sides;

log 1.129=APR*log 2.71828

APR=log 1.129/log 2.71828

=12.13%(Approx).