Question

Calculate the future value of $6,000 in

a. 5 years at an interest rate of 10% per year (round to the nearest dollar)

b. 10 years at an interest rate of 10% per year (round to the nearest dollar)

c. 5 years at an interest rate of 20% per year (round to the nearest dollar)

d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)? (choose from the four options below)

1. The annual interest rate in part (b) is slightly higher than the rate assumed in part (a). This is because of compunding.

2. The amount of interest earned in part (a) is really half of the amount of interest earned in part (b) since in part (b) the money grows for twice as many years as in part (a)

3. The interest earned in part (a) is based on a lower effective annual interest rate.

4. This results because you earn more interest on past interest. As interest is earned on the increasing amount of accumulated interest, the money grows faster as time goes on.

Answer 1

Given the amount of present value is $6,000

We know that the formula for future value calculation is as follows

FV = PV (1+r)ⁿ

Where FV = Future Value

PV = Prsent Value

r = Rate of interest

a) Future Value = 6000 * 1.1⁵ = 9663

b) Future value = 6000 * 1.1¹⁰ = 15562.45

c) Future Value = 6000 *1.2⁵ = 14929.92

Before we move into the four options let me explain the why compounding earns more returns when the time passes the interest on interest increases even the rate does not change.

Let me explain interest and interest on interest with the below table.

Year	Opening Principal	Compound Interest	Closing	Simple Interest	Interest on interest
1	6000.0	600.0	6600.0	600.0	0.0
2	6600.0	660.0	7260.0	600.0	60.0
3	7260.0	726.0	7986.0	600.0	126.0
4	7986.0	798.6	8784.6	600.0	198.6
5	8784.6	878.5	9663.1	600.0	278.5
6	9663.1	966.3	10629.4	600.0	366.3
7	10629.4	1062.9	11692.3	600.0	462.9
8	11692.3	1169.2	12861.5	600.0	569.2
9	12861.5	1286.2	14147.7	600.0	686.2
10	14147.7	1414.8	15562.5	600.0	814.8

Interest on interest on the first 5 years will be 663 and in the next 5 years will be 2899 hence interest is growing faster in the next 5 years compared to the first 5 years hence the amount of interest earned in part (a) less than half the amount of interest earned in part (b)

So the best suitable option is Option -4

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