Question

1. Discuss the concept of interest rate compounding. Why does it matter?

2. Consider an interest rate that is quoted at 8% - what is the equivalent rate if it is compounded

a. Daily

b. Monthly

c. Semi-annually

3. What are the practical implications of the compounding period?

Answer 1

1. The effective annual rate increases with the number of compounding and subsequently the future value also increases. It matters because the future value can increase or decrease on the basis of the number of compounding..

2. a) m = number of compounding
n = number of years
EAR = ( 1 + APR/n)^mn-1
EAR = ( 1+8%/365)³⁶⁵-1 = 8.33%

b)EAR = ( 1+8%/12)¹²-1 = 8.30%

c) EAR = ( 1+8%/2)²-1 = 8.16%

3. The practical implication is seen in case of bonds where semiannual bonds have different value from annual bonds. Bank deposits paying quarterly will pay more than bank with annual compounding

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