Question

Fund A earns interest at a nominal rate of 6% compounded monthly. Fund B earns interest at a nominal rate of discount compounded three times per year. The annual effective rates of interest earned by both funds are equivalent. Calculate the nominal rate of discount earned by Fund B.

Answer 1

Answer: 6.045%

Explanation:

There are two forms of an interest rate: nominal interest rate and effective interest rate. The nominal interest rate does not take into account the compounding period while the effective interest rate does so it is a more accurate measure of interest charges.

The relationship between nominal annual rate (r) and effective annual interest rate (i) is:

i = [ 1 + (r ÷ m) ] ^ m – 1

And r = [ [ (i + 1) ^ (1 ÷ m) ] - 1 ] x m

where "m" is the number of compounding periods per year.

So for the fund A, i(A) = [ 1 + (6% ÷ 12) ] ^ 12 – 1 = 6.17% (m = 12 as the nominal rate of fund A is compounded monthly)

As the annual effective rates of interest earned by both funds are equivalent, i(A) = i(B) = 6.17%

rB= [ [ (iB + 1) ^ (1 ÷ 3) ] - 1 ] x 3 = [ [ (6.17% + 1) ^ ( 1 ÷ 3) ] - 1 ] x 3 = 6.045% (m=3 as the nominal rate of discount of fund B is compounded 3 times per year)