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 and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.):

 Standard rate (APR) % Number of times Compounded Effective Rate (EAR) semiannually 11.3% Monthly 12.2% Weekly 9.9% Infinite 13.6%

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

0.113=(1+APR/2)^2-1

(1+0.113)=(1+APR/2)^2

(1.113)^(1/2)=(1+APR/2)

APR=[(1.113)^(1/2)-1]*2

=11%(Approx).

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

0.122=(1+APR/12)^12-1

(1+0.122)=(1+APR/12)^12

(1.122)^(1/12)=(1+APR/12)

APR=[(1.122)^(1/12)-1]*12

=11.57%(Approx).

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

0.099=(1+APR/52)^52-1

(1+0.099)=(1+APR/52)^52

(1.099)^(1/52)=(1+APR/52)

APR=[(1.099)^(1/52)-1]*52

=9.45%(Approx).

4.EAR=(e)^APR-1
where e=2.71828

0.136=(2.71828)^APR-1

(1+0.136)=(2.71828)^APR

1.136=(2.71828)^APR

Taking log on both sides;

log 1.136=APR*log 2.71828

APR=log 1.136/log 2.71828

=12.75%(Approx).

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