Suppose there are two investment opportunities: “Instrument A” and “Instrument B”. If instrument A offers 14.2% of interest compounded semi-annually and instrument B offers 14% of interest compounded quarterly.

a. Which instrument would you choose as an investor? Why? Explain and show your calculation.

b. Suppose A and B are two different banks that you are going to take out a loan. Which bank would you prefer as a borrower? Why? Explain.

The question asks us to calculate the effective interest rate which takes into account the effect of compounding.

The formula for calculating effective interest rate is =

{(1 + Interest rate/compounding frequency)^Compounding frequency} - 1

For Instrument A

Interest rate = 14.2%

Compounding frequency = semi annually = 2 (Times a year)

{(1 + Interest rate/compounding frequency)^Compounding frequency} - 1

{(1 + 14.2%/2)^2} - 1

{(1 + 7.1%)^2} - 1

1.147041 - 1

0.147041

14.70%

Thus the effective interest rate is 14.70% for Investment A

For Instrument B

Interest rate = 14%

Compounding frequency = quarterly = 4 (Times a year)

{(1 + Interest rate/compounding frequency)^Compounding frequency} - 1

{(1 + 14%/4)^4} - 1

{(1 + 3.5%)^4} - 1

1.147523 - 1

0.147523

14.75%

Thus the effective interest rate is 14.75% for Investment B

A) Being an investor, I would chose the investment which gives me the highest return. On comparing the two schemes, Scheme B has a higher effective interest rate of 14.75% as compared to 14.70% earned on B. Thus I will choose Scheme B

B) Being a borrower, I would prefer to borrow from the bank which charges me the lowest rate of interest. On comparing the two banks, Scheme A has a lower effective interest rate of 14.70% as compared to 14.75% charged on B. Thus I will choose to borrow from bank A.