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What payment made at the end of each year for 18 years will amount to $16,000 at 4.2% compounded monthly?
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In his post, tutor @Theo solved this problem using a calculator,
and described a methodology solving this problem using calculator.
It is good, but since this website is intended to teach mathematical methods,
I present here mathematical solution with all detailed explanations.
As it is given in the post, this annuity is not standard: the payments are made at the end of each year,
while compounding is made at the end of each month.
Analytic formulas exist only for coinciding schedules of payments and compounding.
But we can use an equivalent standard synchronized scheme, considering payments at the end of each year
and compounding at the end of each year with the annual multiplicative growth rate
1+r = = 1.042818007. (1)
Now we can use a standard formula for such ordinary annuity
FV = . (2)
In this formula, FV is the future value in 18 years; P is the annual payment, the unknown value
which we should find.
We calculate the factor in the formula (2) separately
= = 26.31908947.
Then from formula (2) we find
P = = = 607.93 dollars.
Thus we found out the annual payment value. It is $607.93. ANSWER
Solved.
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My result is precisely consisted with the answer by @Theo.
Now you can solve similar problems mathematically and check them using calculator.
It is a good and reliable strategy.