SOLUTION: Find the amount of each payment that must be made into a sinking fund to accumulate each amount. (Recall, in a sinking fund, payments are made at the end of every interest period

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Question 243838: Find the amount of each payment that must be made into a sinking fund to accumulate
each amount. (Recall, in a sinking fund, payments are made at the end of every interest
period.)
6500; money earns 8% compounded annually; 6 annual payments
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you want to make 6 annual payments at 8% compounded annually and at the end of that you want to have $6,500 in the account.

you are looking for the future value of a payment.

the formula for that would be

FUTURE VALUE OF A PAYMENT

+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+

FV = future value
PMT = payment per time period
i = interest rate per time period
n = number of time periods

In your equation:

FV = 6500
PMT = what you want to find
i = 8% per year
n = 6 years

plug these values into the formula to get:

+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+ becomes:

+6500+=+%28PMT+%2A+%28%281.08%29%5E6-1%29%2F.08%29+ which becomes:

6500 = PMT * (.586874323/.08) = PMT * 7.335929037

Divide both sides of this equation by 7.335929037 to get:

PMT = 886.0500105

here's how it works:

display of numbers is truncated to integer units only. calculation of numbers uses complete amount stored in calculator memory.

end of year 1 = 886
end of year 2 = 886 * 1.08 + 886 = 1842
end of year 3 = 1842 * 1.08 + 886 = 2876
end of year 4 = 2876 * 1.08 + 886 = 3992
end of year 5 = 3992 * 1.08 + 886 = 5198
end of year 6 = 5198 * 1.08 + 886 = 6500

In confirmed the answer is correct by using a financial calculator that does all the heavy work for you.