Jamal plans to retire in 17 years. He is saving $2000 every month in a retirement savings account paying him a long-term interest of 9% compounded monthly. What will be the size of his payments per month from the ordinary simple annuity for 20 years following his retirement?
A) $957 836
B) $1434
C) $8618
D) $333
E) $2000

Question

Quizplus · Accepted Answer

First, calculate the future value of the savings using the formula for the future value of an annuity: FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the monthly interest rate, and n is the total number of payments. Here, P = $2000, r = 9%/12 = 0.0075, and n = 17*12 = 204. Plugging these into the formula gives FV = $2000 * [((1 + 0.0075)^204 - 1) / 0.0075] ≈ $884,073. Next, to find the monthly payment from this amount over 20 years (or 240 months) at the same interest rate, use the annuity payment formula: PMT = FV / [(1 - (1 + r)^-n) / r], where FV is the future value, r is the monthly interest rate, and n is the total number of payments. Plugging in the values gives PMT ≈ $884,073 / [(1 - (1 + 0.0075)^-240) / 0.0075] ≈ $8618.

Jamal Plans to Retire in 17 Years