Question

You are planning to make annual deposits of $5,700 into a retirement account that pays 10 percent interest compounded monthly. How large will your account balance be in 30 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Annual interest rate = 10.00%

Monthly interest rate = 10.00% / 12
Monthly interest rate = 0.8333%

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.008333)^12 - 1
Effective annual rate = 1.1047 - 1
Effective annual rate = 0.1047 or 10.47%

Annual deposit = $5,700
Time period = 30 years

Accumulated sum = $5,700*1.1047^29 + $5,700*1.1047^28 + … + $5,700*1.1047 + $5,700
Accumulated sum = $5,700 * (1.1047^30 - 1) / 0.1047
Accumulated sum = $5,700 * 179.850630
Accumulated sum = $1,025,148.59