SOLUTION: Mrs. Cook made deposits of $950 at the end of every 6 months for 15 years. If interest is 3% compounded monthly, how much will Mrs. Cook have accumulated 10 years after the last de

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Question 1207422: Mrs. Cook made deposits of $950 at the end of every 6 months for 15 years. If interest is 3% compounded monthly, how much will Mrs. Cook have accumulated 10 years after the last deposit?

Answer by ikleyn(52805) About Me  (Show Source):
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Mrs. Cook made deposits of $950 at the end of every 6 months for 15 years.
If interest is 3% compounded monthly, how much will Mrs. Cook have accumulated
10 years after the last deposit?
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The nominal interest is 3% compounded monthly.


It means that the monthly effective growth factor is  (1+0.03/12) = 1.0025.


Then the semi-annual effective growth factor is %281%2B0.03%2F12%29%5E6 = 1.0025%5E6 = 1.01509406308652.


So, we can now write the formula for the future value of the ordinary annuity in 15 years 
with the semi-annual deposits of $950 at the end of every 6 months with the found effective 
rate

    FV = 950%2A%28%281.01509406308652%5E%282%2A15%29-1%29%2F0.01509406308652%29 = 35713.39  (rounded).


In 10 years after that the accumulated amount will be

    35713.39%2A%281+%2B+0.01509406308652%29%5E%282%2A10%29 = 48189.99.


ANSWER.  In 10 years after the last deposit, the accumulated amount will be about 48190 dollars.

Solved.