How much more would you earn in the first investment than in the second investment?

Question

$27,000 invested for 40 years at 12% compounded annually

$27,000 invested for 40 years at 6% compounded annually

Answer 1

To find the earnings for each investment, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

For the first investment:
P = $27,000
r = 12% = 0.12
n = 1 (compounded annually)
t = 40 years

A = 27000(1 + 0.12/1)^(1*40)
A ≈ $1,151,094.84

For the second investment:
P = $27,000
r = 6% = 0.06
n = 1 (compounded annually)
t = 40 years

A = 27000(1 + 0.06/1)^(1*40)
A ≈ $243,342.31

The amount earned in the first investment is $1,151,094.84 - $27,000 = $1,124,094.84
The amount earned in the second investment is $243,342.31 - $27,000 = $216,342.31

Therefore, you would earn $1,124,094.84 - $216,342.31 = $907,752.53 more in the first investment than in the second investment.