Question 1205773: Mr. Thompson wants to make monthly deposits into an annuity for his child so that $10,000 will be available in 8 years. If the interest rate is 8% compounded monthly, find the full deposit.
Answer by ikleyn(52805)   (Show Source):
You can put this solution on YOUR website! .
Mr. Thompson wants to make monthly deposits into an annuity for his child
so that $10,000 will be available in 8 years.
If the interest rate is 8% compounded monthly, find the full deposit.
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If the monthly deposits are made at the end of each month, then 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 = 0.08/12; n = 8*12 = 96.
So, according to the formula (1), you get for the monthly payment
P =  = $74.70.
Answer. The necessary monthly deposit value is $74.70.
Note that of projected $10,000, the total of the deposits will be only 8*12 times $74.70,
i.e. 8*12*74.70 = 7171.20 dollars. The rest is what the account will earn/accumulate in 8 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.
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To make such complicated calculations as they are in this problem,
you should have/use an appropriate calculator for such long formulas.
Ideal choice is MS Excel, if you have it in your computer.
Then you write a formula in a text editor, copy-paste it
into an Excel work-sheet cell and click "enter" - the result is ready
instantaneously.
If you have no MS Excel in your computer, you may find similar
free of charge calculators in the Internet. One such calculator is
www.desmos.com/calculator
It allows you to do the same thing: you write a formula in a text editor,
copy-paste it into this calculator and click "enter" - the result is ready
instantaneously.
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