Finance question - compound investment?

If you put a certain amount of money in the bank every month, say $100 at a rate of 6%, and it's compounded monthly, how do I figure out how much I'll have in 25 years?

CB's calculation correctly shows you how much you'd have if you put $100 in the first month and let it grow for 25 years, but what I think you are asking is how much will you have if you put in $100 EVERY MONTH during that 25 years, not just the first month.

The calculation you need to do to find that is called "future value of an annuity". A spreadsheet program or financial calculator might have a function to do that automatically for you, but here's the formula:

v = p * ((1 + i)^n - 1) / i

p = the amount you put in each period
n = the number of periods
i = the interest rate for each period
v = the value of the account at the end of "n" periods.

In your example,
p=$100
n=300 (12*25, the number of months in 25 years)
i=.005 (6% which is .06 / 12 to get the monthly amount)

So you first take (1+.005) to the 300th power, then subtract 1 from it, then multiply by $100 and divide by .005 to get:

$69,299.40

Bank's will typically quote numbers in APR form. If the amount is compounded monthly, the monthly amount you get would be APR/12. In this case 6%/12 = 0.5%.

To figure out how much you would have at the end, take your principal amount time (1+i)^n, where i is the monthly interest rate and n is the number of compounding periods or months.

$100 * (1 + 0.005) ^ (25 * 12) = $446.50