Question

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

a.	An effective interest of 7% compounded semiannually

b.	An effective interest of 13% compounded monthly

c.	An effective interest of 17% compounded weekly

d.	An effective interest of 8% with continuous compounding

Answer 1

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

0.07=[(1+APR/2)^2]-1

(1+0.07)=[(1+APR/2)^2]

APR=[(1+0.07)^(1/2)-1]*2

=6.882%(Approx)

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

0.13=[(1+APR/12)^12]-1

(1+0.13)=[(1+APR/12)^12]

APR=[(1+0.13)^(1/12)-1]*12

=12.284%(Approx)

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

0.17=[(1+APR/52)^52]-1

(1+0.17)=[(1+APR/52)^52]

APR=[(1+0.17)^(1/52)-1]*52

=15.724%(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

=7.696%(Approx)