SOLUTION: Find the amount of each payment to be made into a sinking fund which earns 5​% compounded quarterly and produces ​$31,000 at the end of 2.5 years. Payments are made at the

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Question 1147891: Find the amount of each payment to be made into a sinking fund which earns
5​% compounded quarterly and produces ​$31,000 at the end of 2.5 years.
Payments are made at the end of each period.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29,    


where  FV is the future value of the account;  P is the quarterly payment (deposit); r is the effective quarterly rate yield 
presented as a decimal; n is the number of deposits (= the number of quarters in 2.5 years, i.e. 10, in this case).


From this formula, you get for the quartely payment 


    P = FV%2A%28r%2F%28%281%2Br%29%5En-1%29%29.     (1)


Under the given conditions, FV = $31,000;  r = 0.05/4;  n = 10.  So, according to the formula (1), you get for the monthly payment 


    P = 31000%2A%28%28%280.05%2F4%29%29%2F%28%281%2B0.05%2F4%29%5E10-1%29%29%29 = $2929.60.


Answer.  The necessary monthly deposit value is $2929.60.

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On Ordinary Annuity saving plans,  see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.

The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.

When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.