Question

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

a.	An effective interest of 9% compounded semiannually
b.	An effective interest of 15% compounded monthly
c.	An effective interest of 10% compounded weekly
d.	An effective interest of 8% with continuous compounding

Answer 1

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

0.09=[(1+APR/2)^2]-1

(0.09+1)=[(1+APR/2)^2]

APR=[(0.09+1)^(1/2)-1]*2

=8.81%(Approx)

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

0.15=[(1+APR/12)^12]-1

(1+0.15)=[(1+APR/12)^12]

APR=[(1+0.15)^(1/12)-1]*12

=14.06%(Approx)

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

0.1=[(1+APR/52)^52]-1

(1+0.1)=[(1+APR/52)^52]

APR=[(1+0.1)^(1/52)-1]*52

=9.54%(Approx)

d.EAR=(e)^APR-1

where e=2.71828

0.08=(2.71828)^APR-1

1.08=2.71828^APR

Taking log on both sides;

log 1.08=APR*log 2.71828

APR=log 1.08/log 2.71828

=7.7%(Approx).