Question

An investment pays you an annual 20% nominal interest rate compounded semiannually (10 percent twice a year). A second investment of equal risk has a different annual nominal interest rate but interest is compounded monthly (12 times a year). What nominal annual interest rate on the second investment would you have to receive to make you indifferent between the two investments?

Answer 1

Equivalent rate of Semiannual Compounding = Equivalent Rate of Monthly Compounding
(1+20%/2)^2-1 = (1+APR/12)^12 -1
1.1^2 = (1+APR/12)^12
APR/12 = 1.21^1/12-1
APR or rate which will create indifference = 12*(1.21^1/12-1) = 19.21%

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