Question

How much more interest is earned on a $40 000 investment if the interest at 6% p.a. is compounded annually over 6 years, compared to simple interest at 6% p.a. earned over the same time?

Answer 1

$ 4,740.76

Explanation:

The general formula for compound interest computation is

`A = P(1 + r)^t`

where
A = amount accrued

r = annual interest rate as a decimal

t = number of years

Given
P = 40,000
r = 6% = 6/100 = 0.06
n = 6 years

A = 40000(1 + 0.06)⁶
= 40000 (1.06)⁶
= 40,000 X 1.418519112256
= $56,740.76

Interest obtained
= A - P
= $56,740.76 - 40,000.00

= $16,740.76

For simple interest the formula for interest is
I = Prt
where once again

P = amount invested
I = interest earned
r = annual interest rate in decimal
t = number of years

Plugging in values for P, r, t we get
I = 40000 x 0.06 x 5 = $ 12,000.00

So the amount of interest earned if 40,000 is compounded annually at 6% for 5 years
= $16,740.76 - $12,000
= $4,740.76