An employee put $4,000.00 in a retirement account that offers 8% 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 6 years?
A $6,347.50$6,347.50
B $320.00$320.00
C $1,920.00$1,920.00
D $2,347.50
To calculate the interest earned, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/retirement account
P = the principal amount (initial deposit)
r = annual interest rate expressed as a decimal
n = number of times that interest is compound per year
t = number of years
In this case, the principal amount (P) is $4,000.00, the interest rate (r) is 8% or 0.08, the number of times interest is compounded per year (n) is 1, and the number of years (t) is 6.
Applying the values to the formula:
A = 4000(1 + 0.08/1)^(1*6)
A = 4000(1 + 0.08)^6
A = 4000(1.08)^6
A ≈ 4000(1.593)
A ≈ $6,372.00
So the amount closest to the interest earned at the end of 6 years is $6,372.00 which is closest to option A, $6,347.50. Therefore, the answer is A.