How much more would you earn in the first investment than in the second investment?
$28,000 invested for 40 years at 10% compounded annually
$28,000 invested for 40 years at 5% compounded annually
To calculate the amount earned in the first investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
For the first investment:
P = $28,000
r = 10% = 0.10
n = 1 (compounded annually)
t = 40 years
A = 28000(1 + 0.10/1)^(1*40)
A = 28000(1.1)^40
A ≈ $1,454,498.62
Now, let's calculate the amount earned in the second investment:
For the second investment:
P = $28,000
r = 5% = 0.05
n = 1 (compounded annually)
t = 40 years
A = 28000(1 + 0.05/1)^(1*40)
A = 28000(1.05)^40
A ≈ $132,268.15
The difference in earnings between the two investments is:
$1,454,498.62 - $132,268.15 = $1,322,230.47
Therefore, the first investment would earn approximately $1,322,230.47 more than the second investment.