one such calculator can be found here.
http://arachnoid.com/finance/index.html
using this calculator, you would divide the annual percentage rate by 12 to get the monthly percentage rate.
you would multiply the number of years by 12 to get the number of months.
you would enter the monthly payment as a negative number (it's what you are paying out, so it's negative).
you would leave the present value and future value as 0.
you would set the payments to be at the end of the period (this is usually what is done).
you would then click on the FV button and it will tell you how much money you would have at the end of the 15 year period.
the assumption is that all interest earned in the intermediate years is re-invested immediately into the annuity fund.
your results will be as shown below:
the first one shows 90 invested monthly.
the second one shows 110 invested monthly.
the link to the calculator also shows the formulas used.
they can be a bit hard to follow, but they'll give you the same answer if you give them the right information.
the formulas work from the interest rate and not the interest percentage rate.
basically you take the percentage rate and divide it by 100 to get the rate.
the key is in the time intervals involved.
with monthly compounding, the annual rate is divided by 12 and the number of years if multiplied by 12.
the actual month by month calculations are shown in the following spreadsheet.
only the first several months are shown, and then only the last several months are shown.
the stuff in the middle is just more of the same.
multiplying the previous month's remaining balance by (1 + .08/12) gives you the previous month's remaining balance plus the interest that is earned by it.
you then add the monthly payment to that to get the current month's remaining balance.
you can see that the spreadsheet analysis and the financial formulas give you the same result.