SOLUTION: A man will deposit with a trust company a sum just sufficient to provide his family with an annuity of 750 dollars per month for 15 years. How much does he deposit if the fund accu

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Question 1167591: A man will deposit with a trust company a sum just sufficient to provide his family with an annuity of 750 dollars per month for 15 years. How much does he deposit if the fund accumulates at {4 1/2%, m=12}?
Answer by ikleyn(52781) About Me  (Show Source):
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A man will deposit with a trust company a sum just sufficient to provide his family with an annuity
of 750 dollars per month for 15 years. How much does he deposit if the fund accumulates at {4.5%, m=12}?
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In this problem, they talk about the sinking fund, which is a monthly compounded account.  It provides 
monthly outpayments of $750 every month during 15 years. The account is compounded monthly at the annual 
rate of 4.5%.


They want you find the starting (= the original) amount of money in the fund.


The total outpayment from the fund in 15 years is

    Total = 750*12*15 = 135000  dollars.


To answer the problem's question, we should calculate the Present Value of this amount.
The Present Value is

    PV = 135000%2F%281%2B0.045%2F12%29%5E%2812%2A15%29 = 68822.95.


Thus the problem is just solved.


The initial amount in the fund must be (at least) $68,822.95.    ANSWER


Then the fund will be able to pay out $750 every month during 15 years.

Solved.