Question

You plan to invest Rs. 2000 in a fixed deposit today that pays a stated annual interest rate of 8 percent which is expected to apply to all future years.

a) How much will you have in the account at the end of 10 years if interest is compounded as follows

i) Annually ii) Semiannually iii)Monthly

b) What is the effective annual rate (EAR) for each compounding frequency in part a ?

Answer 1

Answer : Calculation of Future Value when Compounded

(i.) Annually

Future Value = Present Value * (1 + rate per period )^number of compounding period

rate per period is 0.08

number of Compounding period i.e 10

Future Value = 2000 * (1 + 0.08 )^10

= 2000 * 2.158925

= 4317.85

(ii.)Semi Annually

Future Value = Present Value * (1 + rate per period )^number of compounding period

rate per period is 0.08 / 2 = 0.04 (Divided by 2 as componded semiannually)

number of Compounding period i.e 10 * 2 = 20 (Multiplied by 2 as componded semiannually)

Future Value = 2000 * (1 + 0.04 )^20

= 2000 * 2.191123

= 4382.27

(iii.) Monthly

Future Value = Present Value * (1 + rate per period )^number of compounding period

rate per period is 0.08 / 12 = 0.0066667 (Divided by 12 as componded semiannually)

number of Compounding period i.e 10 * 12 = 120 (Multiplied by 12 as componded semiannually)

Future Value = 2000 * (1 + 0.0066667 )^120

= 2000 * 2.21964

= 4439.28

(b.) Effective Rate

Effective Rate = [(1 + rate per period )^number of compounding period] - 1

In case of Annual Compounding = 0.08 or 8%

In case of Semiannual Compounding

Effective Rate = [1 + (0.04)^2] - 1 = 8.16%

In case of Monthly Compounding

Effective Rate = [1 + (0.0066667)^12] - 1 = 8.30%