An employee put $12,000.00 in a retirement account that offers 7% interest compounded annually. The employee makes no additional deposits or withdrawals. Which amount is closest to the interest the employee will have earned at the end of 15 years?
$2,110.84
$21,108.38
$12,600.00
$33,108.38
The formula to calculate the compound interest is: A = P(1 + r/n)^(nt) - P, where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time the money is invested/borrowed for, in years
Given:
P = $12,000
r = 7% or 0.07
n = 1 (compounded annually)
t = 15 years
Plugging in the values:
A = $12,000(1 + 0.07/1)^(1*15) - $12,000
A = $12,000(1.07)^15 - $12,000
A = $12,000(2.759543) - $12,000
A = $33,114.52 - $12,000
A = $21,114.52
Therefore, the amount closest to the interest earned at the end of 15 years is $21,114.52, which rounds to $21,108.38. So, the closest amount is $21,108.38.