SOLUTION: If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?

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Question 1165395: If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?
Answer by ikleyn(52781) 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,    (1)


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).


Under the given conditions, P = 750;  r = 0.08/2;  n = 2*10 = 20.  So, according to the formula (1), you get at the end of the 10-th year


    FV = 750%2A%28%28%281%2B0.08%2F2%29%5E%282%2A10%29-1%29%2F%28%280.08%2F2%29%29%29 = 750%2A%28%281.04%5E20-1%29%2F0.04%29 = $22,333.56.


Note that you deposit only  2*10*$750 = $15,000.  The rest is what the account earns/accumulates in 10 years.

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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.