Compound interest question?

Question

A couple invests $300 per month in a fund. How much will they have after 10 years if the per annum rate of return of the fund is assumed to be 9% compounded monthly?

Thank you for your help!

Answer 1

That would be a great fund. The formula is:

A = {PMT[(1+ APR/n)^nY-1]} / (APR/n)

PMT = 300, APR = 0.09, n=12, Y = 10

A = 300[(1+0.09/12)^120 - 1] / (0.09/12)

A = $58054.28
Not bad for only putting in $36,000 of their own money!

Answer 2

This is a nice example of an annuity.
Only question: Do they invest the money at the
beginning of each month or at the end of each month?
It makes a difference in the final future value!
Let's assume they invest it at the end of each month,
i.e., it's an ordinary annuity.
The formula for an ordinary annuity is
S = R/i *( (1+i)^n -1),
where
S is the future value
R is the amount paid per month
n is the number of payment and interest periods
i is the interest rate.
So, let's plug in the numbers and grind away!
R = 300
i = .09/12 = 0.0075
(we must use the monthly interest rate here)
n = 120 (there are 120 payment periods)
S = 300/(0.0075) * ( 1.0075^120 -1)
which gives us
S = 58054.28
I'll check this on my graphing calculator also.
I don't have it available right now!