Question

Find the APR, or stated rate, in each of the following cases:

a.	An effective interest of 16% compounded semiannually

b.	An effective interest of 18% compounded monthly

c.	An effective interest of 14% compounded weekly

d.	An effective interest of 9% with continuous compounding

Answer 1

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

0.16=[(1+APR/2)^2]-1

(1+0.16)=[(1+APR/2)^2]

APR=[(1+0.16)^(1/2)-1]*2

=15.41%(Approx)

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

0.18=[(1+APR/12)^12]-1

(1+0.18)=[(1+APR/12)^12]

APR=[(1+0.18)^(1/12)-1]*12

=16.67%(Approx)

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

0.14=[(1+APR/52)^52]-1

(1+0.14)=[(1+APR/52)^52]

APR=[(1+0.14)^(1/52)-1]*52

=13.12%(Approx)

d.EAR=(e)^APR-1

where e=2.71828

0.09=(2.71828)^APR-1

1.09=(2.71828)^APR

Taking log on both sides;

log 1.09=APR*log 2.71828

APR=log 1.09/log 2.71828

=8.62%(Approx)