Question

Recently, Money Money 4U offered an annuity that pays 5.4% compounded monthly. If $1,540 is deposited into this annuity every month, how much is the account after 10 years? How much of this is interest?

Type the amount in the account: $ _______

(Round to the nearest dollar.)

Answer 1

Monthly deposit = $1,540

Annual interest rate = 5.40%
Monthly interest rate = 5.40% / 12
Monthly interest rate = 0.45%

Time period = 10 years or 120 months

Accumulated sum = $1,540*1.0045^119 + $1,540*1.0045^118 + …. + $1,540*1.0045 + $1,540
Accumulated sum = $1,540 * (1.0045^120 - 1) / 0.0045
Accumulated sum = $1,540 * 158.650979
Accumulated sum = $244,323

Balance in the account is $244,323

Total amount deposited = 120 * $1,540
Total amount deposited = $184,800

Total interest earned = Accumulated sum - Total amount deposited
Total interest earned = $244,323 - $184,800
Total interest earned = $59,523