SOLUTION: Joan is saving for a new stereo in 3 years that costs 1500$. How much does she need to deposit at the end of every month in an account that earns interest at 4.5%, compounded month

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Question 1144992: Joan is saving for a new stereo in 3 years that costs 1500$. How much does she need to deposit at the end of every month in an account that earns interest at 4.5%, compounded monthly
Answer by ikleyn(52802) About Me  (Show Source):
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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 monthly payment (deposit); r is a nominal 
monthly percentage yield presented as a decimal; n is the number of deposits (= the number of years multiplied by 12, in this case).


From this formula, you get for the monthly payment 


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


Under the given conditions, FV = $1500;  r = 0.045/12;  n = 3*12.  So, according to the formula (1), you get for the monthly payment 


    P = 1500%2A%28%28%280.045%2F12%29%29%2F%28%281%2B0.045%2F12%29%5E%283%2A12%29-1%29%29%29 = 38.996 dollars = round it ! = 39 dollars.


Answer.  The necessary monthly deposit value is 39 dollars..

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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.