Starting at the age of 30, at the end of each month, you invest $540 into a retirement IRA (individual retirement account). The IRA guarantees an APR of 9% compounded monthly for the life of the account. How much money will you have in the account when you turn 65? Give your answer as a decimal rounded to the nearest hundredth.
A) $504000.00
B) $1588563.62
C) $1708965.24
D) $1974965.87
E) None of the above.

Question

Starting at the age of 30, at the end of each month, you invest $540 into a retirement IRA (individual retirement account). The IRA guarantees an APR of 9% compounded monthly for the life of the account. How much money will you have in the account when you turn 65? Give your answer as a decimal rounded to the nearest hundredth. 
A) $504000.00
B) $1588563.62
C) $1708965.24
D) $1974965.87
E) None of the above.

Quizplus · Accepted Answer

The future value of an annuity is given by the formula:FV = P * (((1 + r/n)^(n*t)) - 1) / (r/n))where:P is the periodic paymentr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:P = $540r = 9% = 0.09n = 12 (monthly compounding)t = 35 (65 - 30)Plugging these values into the formula, we get:FV = 540 * (((1 + 0.09/12)^(12*35)) - 1) / (0.09/12))= 540 * (((1.0075)^420) - 1) / (0.0075))= 540 * (2.999 - 1) / (0.0075)= 540 * 1.999 / 0.0075= $1,588,563.62Therefore, the correct answer is B) $1,588,563.62.

Starting at the Age of 30, at the End of Each