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. Use 365 days in a year.)

Stated Rate (APR)	Number of Times Compounded	Effective Rate (EAR)
%	Semiannually		13.50	%
%	Monthly		9.50
%	Weekly		11.50
%	Daily		9.50

Answer 1

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

1.

0.135=(1+APR/2)^2-1

(0.135+1)=(1+APR/2)^2

(1.135)^(1/2)=(1+APR/2)

APR=[(1.135)^(1/2)-1]*2

=13.07%(Approx).

2.

0.095=(1+APR/12)^12-1

(0.095+1)=(1+APR/12)^12

(1.095)^(1/12)=(1+APR/12)

APR=[(1.095)^(1/12)-1]*12

=9.11%(Approx).

3.

0.115=(1+APR/52)^52-1

(0.115+1)=(1+APR/52)^52

(1.115)^(1/52)=(1+APR/52)

APR=[(1.115)^(1/52)-1]*52

=10.90%(Approx).

4.

0.095=(1+APR/365)^365-1

(0.095+1)=(1+APR/365)^365

(1.095)^(1/365)=(1+APR/365)

APR=[(1.095)^(1/365)-1]*365

=9.08%(Approx).