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How much must be deposited at the end of each month for 3.5 years to accumulate
1801.00 dollars at 8% compounded monthly?
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This is a standard ordinary annuity saving plan accumulating money.
They want you determine the value of the monthly deposit.
Start from the formula for the future value of an ordinary annuity
FV = ,
where FV is the future value of the account; P is the monthly payment (deposit);
r is the monthly effective rate of compounding 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 the formula for the monthly payment
P = . (1)
Under the given conditions, FV = $1801; r = 0.08/12; n = 3.5*12 = 42.
So, according to the formula (1), you get for the monthly payment value
P = = 37.29926133, or 37.30 dollars rounded to closest greater cent.
Answer. The necessary monthly deposit value is $37.30.
Solved.
An important moment in such calculations is to make them with high precision
and do not make rounding at intermediate steps. Rounding should be done only once at the end.
In my calculations, I used MS Excel software in my computer, which works with 15 decimal places
after the decimal dot. It does provide the necessary precision.