[Solution] 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
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).