SOLUTION: How much should a family deposit at the end of every 6 months in order to have $4000 at the end of 6 years? The account pays 5.3% interest compounded semiannually. (Round your fina

Algebra ->  Finite-and-infinite-sets -> SOLUTION: How much should a family deposit at the end of every 6 months in order to have $4000 at the end of 6 years? The account pays 5.3% interest compounded semiannually. (Round your fina      Log On


   

Question 1127934: How much should a family deposit at the end of every 6 months in order to have $4000 at the end of 6 years? The account pays 5.3% interest compounded semiannually. (Round your final answer to two decimal places.)
Answer by ikleyn(52802) 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 semi-annual payment (deposit); r is the semi-annual percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 2, in this case).


From this formula, you get for for the semi-annual payment 


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


Under the given conditions, FV = $4,000;  r = 0.053/2;  n = 6*2.  So, according to the formula (1), you get for the semi-annual payment 


    P = 4000%2A%28%28%280.053%2F2%29%29%2F%28%281%2B0.053%2F2%29%5E%286%2A2%29-1%29%29%29 = $287.50.


Answer.  The necessary semi-annual deposit value is $287.50.

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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.