SOLUTION: $960 is deposited at the end of every three months into an account that pays 5.1% compounded quarterly. How much interest will the investment earn over 4 years?

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Question 1148190: $960 is deposited at the end of every three months into an account that pays 5.1% compounded quarterly. How much interest will the investment earn over 4 years?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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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,    (1)


where  FV is the future value of the account;  P is your quarterly payment (deposit); r is the quarterly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 4, in this case).


Under the given conditions, P = 960;  r = 0.051/4;  n = 4*4 = 16.  So, according to the formula (1), you get at the end of the 4-th year


    FV = 960%2A%28%28%281%2B0.051%2F4%29%5E%284%2A4%29-1%29%2F%28%280.051%2F4%29%29%29 = $16919.93.


Note that you deposit only  4*4*$960 = $15360.  The difference 

    16919.93 - 15360 = 1559.93 dollars

is the interest which the account earns/accumulates in 4 years.     ANSWER

Solved.

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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.

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