Question

Find the APR, or stated rate, in each of the following cases (Do not round intermediate...

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 10.50%
Monthly 11.4
Weekly 9.1
Infinite 12.8

  

Homework Answers

Answer #1

EAR=(1+APR/m)^m-1

where m=compounding periods

1.

0.105=(1+APR/2)^2-1

(0.105+1)^(1/2)=1+APR/2

Hence

APR=[(0.105+1)^(1/2)-1]*2

=10.24%

2.

0.114=(1+APR/12)^12-1

Hence

APR=[(1+0.114)^(1/12)-1]*12

which is equal to

=10.84%(Approx).

3.

0.091=(1+APR/52)^52-1

Hence

APR=[(1+0.091)^(1/52)-1]*52

which is equal to

=8.72%(Approx)

4.

EAR=(e^APR)-1

where e=2.71828

0.128=(2.71828^APR)-1

(1+0.128)=2.71828^APR

Taking log on both sides;

log 1.128=APR*log 2.71828

Hence APR=log 1.128/log 2.71828

which is equal to

=12.04%(Approx).

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