Heather is planning to retire in 10 years. She will then need an income of $1,500 at the end of every month for the subsequent 25 years. She is going to make one investment today to provide all of the money she will eventually collect. Her investments will earn 12% compounded monthly. How much should she invest today?

A) $43,152.46
B) $67,449.00
C) $92,461.46
D) $139,437.52
E) $167,687.74

Question

Stella Christian · Accepted Answer

Final Answer : A, Explanation :  The correct answer is A.The future value of the annuity is:FV = PMT * [(1 + r)^n - 1] / rwhere:PMT = the monthly payment = $1,500r = the monthly interest rate = 12% / 12 = 1%n = the number of months = 25 * 12 = 300FV = $1,500 * [(1 + 0.01)^300 - 1] / 0.01 = $43,152.46The present value of the investment is:PV = FV / (1 + r)^nPV = $43,152.46 / (1 + 0.01)^300 = $167,687.74Therefore, Heather should invest $167,687.74 today.

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