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		14.50	%
%	Monthly		10.50
%	Weekly		10.50
%	Daily		8.50

Answer 1

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

1.

0.145=(1+APR/2)^2-1

(1+0.145)=(1+APR/2)^2

(1.145)^(1/2)=(1+APR/2)

APR=[(1.145)^(1/2)-1]*2

=14.01%(Approx).

2.

0.105=(1+APR/12)^12-1

(1+0.105)=(1+APR/12)^12

(1.105)^(1/12)=(1+APR/12)

APR=[(1.105)^(1/12)-1]*12

=10.03%(Approx).

3.

0.105=(1+APR/52)^52-1

(1+0.105)=(1+APR/52)^52

(1.105)^(1/52)=(1+APR/52)

APR=[(1.105)^(1/52)-1]*52

=9.99%(Approx).

4.

0.085=(1+APR/365)^365-1

(1+0.085)=(1+APR/365)^365

(1.085)^(1/365)=(1+APR/365)

APR=[(1.085)^(1/365)-1]*365

=8.16%(Approx).