Question

Consider a 2-year investment project that provides a compound annual rate of return of 10%.

a) Calculate the corresponding average simple annual rate of return. (2 marks)

b) Calculate the corresponding 2-year rate of return based on the compound rate and the simple rate of return. (3 marks)

c) Explain in words (no calculation should be provided) why the two rates in part (b) are the same. [Hint: Take a close look at the question and identify the key words(s) that points to that result.] (2 marks)

d) In general, under what condition will the future values (with n > 1) calculated using both rates (compound and simple) be the same? Explain.

Answer 1

a) Corresponding Average Simple Annual Rate of Return = [{(1+Compound Annual Rate of Return)^Number of years}-1]/Number of years = [{(1+0.1)^2}-1]/2 = 10.5%

b) Based on Compound rate = [(1+Compound Annual Rate of Return)^Number of Years]-1 = [(1+0.1)^2]-1 = 21%

Based on Simple Rate of Return = Corresponding Average Simple Annual Rate of Return*Number of years = 10.5*2 = 21%

c) Both are same because Simple Rate that we have considered is the "CORRESPONDING SIMPLE RATE OF RETURN", calculated on the basis of the EFFECTIVE ANNUAL AVERAGE RATE derived from the compound Annual Rate of Return.

d) In general, Both rates will be same when, simple rate used for calculation, will be the average rate calculated based on the Effective Average Annual Rate of the Compound Rate of Return.