# Question & Answer: Find the APR, or stated rate, in each of the following cases (Do not round intermediate calculations. Enter your answers as…..

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.):

Effective Rate (EAR) Number of Times Compounded Semiannually Monthly Weekly Infinite Stated Rate e (APR) 12.0 9.7 12.4

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

where m=compounding periods

1.

0.111=(1+APR/2)^2-1

(1+0.111)^(1/2)=1+APR/2

Hence APR=[(1+0.111)^(1/2)-1]*2

=10.81%(Approx).

2.

0.12=(1+APR/12)^12-1

APR=[(1.12)^(1/12)-1]*12

=11.39%(Approx).

3.

0.097=(1+APR/52)^52-1

APR=[(1.097)^(1/52)-1]*52

=9.27%(Approx).

4.

EAR=e^APR-1

where e=2.71828

0.134=2.71828^APR-1

1.134=2.71828^APR

Taking log on both sides;

log 1.134=APR*log 2.71828

Hence APR=log 1.134/log 2.71828

=12.58%(Approx).