Question

Calculate the future value of $ 9,000 in

a. 5 years at an interest rate of 5 % per year.

b. 10 years at an interest rate of 5 % per year.

c. 5 years at an interest rate of 10 % per year.

d. Why is the amount of interest earned in part ​(a​) less than half the amount of interest earned in part ​(b​)?

Answer 1

Future Value (FV)  = Present Value * (1 + interest rate%)ⁿ

Present value = $9000

1. Interest rate or r = 5%

Time or n = 5,

as per the above formula

FV= 9000(1+0.05)⁵

FV= 9000* 1.276

FV= $11,486.53

Interest earned = 11486-9000= $ 2486.53

2. Interest rate or r = 5%

Time or n = 10,

as per the above formula

FV= 9000(1+0.05)¹⁰

FV= 9000* 1.6288

FV= $14, 660.05

Interest earned = 14660.05 - 9000= $ 5660.05

3. Interest rate or r = 10%

Time or n = 5,

as per the above formula

FV= 9000(1+0.10)⁵

FV= 9000* 1.6105

FV= $14494.59

Interest earned = 14494.59- 9000= $ 5494.59

4. The interest earned is not constant here. Because the interest that is earned in the first year will be added to the principal amount for the next year thus increasing the mount deposited, so the interest yearned in the second year is comparatively higher the interest earned in 1^st year. That why, because of compounding even though the time has been doubled, the interest earned is more than double.