3. You have saved $130,000 in a retirement account, and you are about to retire.

Question

3. You have saved $130,000 in a retirement account, and you are about to retire. In order to ensure you have a regular stream of money coming in, you have decided to give the $130,000 to an investment firm in exchange for their agreement to pay you $1,000 at the end of every month. If the annual interest rate is 4.8%, for how many months does the investment firm have to make payments to you in order for this arrangement to be a good deal for you? Round your answer to the nearest whole number of months. [Hint: Is $130,000 the present or future value of an annuity? Which of the four variables are you solving?]

Explanation / Answer

$ 130,000 is the present value of the annuity.

And we are solving for n ?

Annuity = $ 1,000.

r = 0.048 / 12 = 0.004 %

n = ?

Present value of an annuity = Annuity x [ { 1 - ( 1 / 1 + r) n } / r ]

or 1,000 x [ { 1 - ( 1 / 1 + 0.004)n } / 0.004] = 130,000

{1 - ( 1/ 1 + 0.004) n } / 0.004} = 130

or n = 183 months

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