Question

(Compound interest with non-annual periods )

You just received a bonus of 2,000.

a. Calculate the future value of 2,000 given that it will be held in the bank for 5 years and earn an annual interest rate of 4 percent

.b. Recalculate part (a ) using a compounding period that is (1) semiannual and (2) bimonthly.

c. Recalculate parts (a ) and (b )using an annual interest rate of 8 percent.

d. Recalculate part (a ) using a time horizon of 10 years at an annual interest rate of 4 percent

.e. What conclusions can you draw when you compare the answers in parts (c ) and (d ) with the answers in parts (a ) and (b )?

(Round to the nearest cent.)

Answer 1

(a) Initial Investment (Bonus Received) = $ 2000, Tenure = 5 years and Interest Rate = 4 %

Future Value = FV5 = 2000 x (1.04)^(5) = $ 2433.306 ~ $ 2433.31

(b) Semi-Annual Compounding:

Applicable Interest Rate = (4/2) = 2 % per half-year and Tenure = 5 x 2 = 10 years

Future Value = 2000 x (1.02)^(10) = $ 2437.99

Bimonthly:

Applicable Interest Rate = (4/24) = 1/6 % or 0.1667 % and Half-Month Tenure = (12 x 2 x 5) = 120 months

Future Value = 2000 x (1.001667)^(120) = $ 2442.496 ~ $ 2442.49

(c) Annual:

Tenure = 5 years and Applicable Interest Rate = 8 %

Initial Investment = $ 2000

Future Value = 2000 x (1.08)^(5) = $ 2938.66

Semi-Annual:

Tenure = 5 years or (5 x 2) = 10 half-years and Applicable Interest Rate = 8 / 2 = 4 %

Future Value = 2000 x (1.04)^(10) = $ 2960.49

Bimonthly:

Tenure = 5 years or (5 x 12 x 2) = 120 months and Applicable Interest Rate = (8/24) = 0.33 %

Future Value = 2000 x (1.0033)^(120) = $ 2969.802 ~ $ 2969.8

(d) Tenure = 10 years and Annual Interest Rate = 4 %

Initial Investment = $ 2000

Future Value = 2000 x (1.04)^(10) = $ 2960.49

NOTE: Please raise a separate query for the solution to the last sub-part as one query is restricted to the solution of only one complete question with upto a maximum of four sub-parts.