An employee put $8,500.00 in a retirement account that offers 6% 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?
$11,870.74
$16,150.00
$20,370.74
$7,650.00
$20,370.74
To calculate the total amount in the retirement account after 15 years, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial amount of money)
r = annual interest rate (decimal)
n = number of times interest applied per time period
t = time the money is invested for in years
In this case:
P = $8,500.00
r = 0.06
n = 1 (compounded annually)
t = 15
A = $8,500(1 + 0.06/1)^(1*15)
A = $8,500(1 + 0.06)^15
A = $8,500(1.06)^15
A = $8,500(2.279910)
A = $19,348.24
The interest earned would be the total amount in the retirement account after 15 years minus the initial $8,500.00 deposit:
$19,348.24 - $8,500.00 = $10,848.24
Therefore, the closest amount to the interest earned would be $20,370.74.