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Three friends want $3,000,000 at the end of 10 years. How much money
should they put into an account each month that pays 7% annual interest
compounded monthly?
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If the deposit is made regularly at the end of each month, such saving plan is called
an Ordinary Annuity. The general formula for such a plan 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 = $3,000,000; r = 0.07/12; n = 10*12 = 120.
So, according to the formula (1), you get for the monthly payment
P = = $17,332.55.
Answer. The necessary monthly deposit value is $17,332.55.
Note that of projected $3,000,000, the total of deposits will be only 10*12 times $17,332.55,
i.e. about 10*12*17332.55 = 2079906 dollars. The rest is what the account will earn/accumulate 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.