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?
Responses
A $6,347.50$6,347.50
B $320.00$320.00
C $1,920.00$1,920.00
D $2,347.50
The formula to find the amount of interest earned on an investment with compound interest is:
A = P(1 + r/n)^(nt) - P
Where:
A = the future value of the investment
P = the principal amount (the initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount is $4,000, the annual interest rate is 8% (or 0.08 as a decimal), the interest is compounded annually (so n = 1), and the number of years is 6.
Plugging these values into the formula:
A = 4000(1 + 0.08/1)^(1*6) - 4000
A = 4000(1 + 0.08)^6 - 4000
A = 4000(1.08)^6 - 4000
Calculating this using a calculator:
A ≈ 6347.50
Therefore, the interest earned at the end of 6 years is closest to $6,347.50.
The closest response from the given options is A: $6,347.50.