Hi, might be too late but have just spent a lot of time myself with a similar compounding interest problem. I ended up finding a solution online. this is just compound interest though, an example of an annuity would be "$100 invested every month for 10 years at 5% interest.
Here is the formula:
Compounding Interest Formula (Monthly) A = P (1 + r/n) ^n*t
...where "A" is the ending amount, "P" is the beginning amount (or "principal"), "r" is the interest rate (expressed as a decimal), "n" is the number of compoundings a year, and "t" is the total number of years.
For my question:
$10,000 invested for 10 years earning 5% interest, compounding monthly (12 times per year)
10000 x (1 + 0.05/12) ^ (12 x 10) = 16470.09 (Total) Return = $6470.09
