Question 1148462: Mr. Nakamura wants to make monthly deposits into an annuity for his grandchild so that $10,000 will be available in 6 years. If the interest rate is 9% compounded monthly, find the monthly deposit. (Round your final answer to two decimal places.)
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Thanks to @MathTherapy, who noticed my fault.
I re-edited / re-calculated my post, and a renewed / corrected version is below.
It is a classic Ordinary Annuity saving plan. The general formula is
FV =  ,
where FV is the future value of the account; P is the monthly payment (deposit); r is the 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 =  . (1)
Under the given conditions, FV = $10,000; r = 0.09/12; n = 6*12. So, according to the formula (1), you get for the monthly payment
P =  = $105.26.
Answer. The necessary monthly deposit value is $105.26.
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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.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Mr. Nakamura wants to make monthly deposits into an annuity for his grandchild so that $10,000 will be available in 6 years. If the interest rate is 9% compounded monthly, find the monthly deposit. (Round your final answer to two decimal places.)
IKLEYN made a mistake.
A monthly payment of $51.68 would be enough for TEN (10) years, which is what she calculated.
However, a monthly payment of $105.26 would be enough for SIX (6) years, which is what is needed.
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