SOLUTION: I have been diligently working on the following problem, but I jsut cannot seem to come up with the correct answer: Find the monthy payment that will yield the future value of $25

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Question 248886: I have been diligently working on the following problem, but I jsut cannot seem to come up with the correct answer:
Find the monthy payment that will yield the future value of $250,000 using an ordinary annuity at 11% for 39 years (Round your number to the nearest cent).
On my last attempt I came up with: 250,000(0.09)/(1+0.09)^39-1 and it was still incorrect. Any light you could shed would be greatly appreciated. Thank you in advance.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
annuity payment is equal to x.
future value is equal to 250000
annual interest = 11%

the assumption is that monthly compound interest is being used.

this means that you have to convert your annual interest rate to monthly interest rate.

it also means you have to convert your number of time periods from years to months.

the formula you need would be:

+PMT%28FV%29+=+%28FV+%2F+%28%28%28%28%281%2Bi%29%5En-1%29%29%2Fi%29%29%29+

PMT = Payment per Time Period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods

In your problem:

PMT = x
FV = 250000
i = .11 / 12 = .0091666666667
n = 39 * 12 = 468

you convert your annual interest rate to monthly interest rate by dividing it by 12.

you convert your number of time periods from years to months by multiplying it by 12.

your formula becomes:



your answer becomes:

x = 32.48088508

I confirmed using a financial calculator.

the answer is valid except that the financial calculator returned an answer of x = 32.1858482

i'm attributing the difference in the answers to rounding.


**************************** NOTE ****************************************

The difference was not due to rounding.

The difference was due to the fact that my financial calculator was set to calculate based on payments at the beginning of the month rather than at the end of the month.

I changed the option and recalculated and got an answer of 32.48088514

This is much closer to the answer of 32.48088508 I got using a scientific calculator based on the formula.

The 32.48088508 number is confirmed fully now.

There's a much smaller difference that is definitely most likely due to rounding.

*************************************end of note****************************

i would go with what your calculator says after you do the operations as indicated above.

your formula was:

250000%280.09%29%2F%281%2B0.09%29%5E39-1

first problem is your formula should have been:

250000+%2F+%28%28%28%281.009166667%29%5E39-1%29%2F.009166667%29%29

second problem is you should have used 468 instead of 39 to get:

250000+%2F+%28%28%28%281.009166667%29%5E468-1%29%2F.009166667%29%29