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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
Expert Answer
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).
