If someone puts $1000 every month for 10 years in an investment account that pays 6% compound interest, how much would they have at the end of the 10 years?
How is the interest compounded? Does 6% per annum equate to 0.5% compounding per month? If so, then the final amount would be $164,698.74
If it’s compounded annually, I get $167,659.71, or a return on investment of 171.5735%.
Ringo, how do you come up with the return on investment of 171%? I’m not good with percentages but out of the $167,000, $120,000 was mine to begin with.
I did the division backwards. Good thing there’s no grade involved. It should be 139.7164%
I liked the first rate much better 
A principle P which is invested at a yearly rate of r, interest compounded n times a year for t years, will grow to P*(1+r/n)[sup]nt[/sup].
So, if you invest some every month, you will end up with a sum of such functions, each with a different time. Let m be the number of subdivisions so that you make m payments of P/m and each payment will have a differing time of -t/m.
P/m*(1+r/n)[sup]nt[/sup] + P/m*(1+r/n)[sup]n(t-t/m)[/sup] + P/m*(1+r/n)[sup]n(t-2t/m)[/sup] + … P/m*(1+r/n)[sup]n(t-mt/m)[/sup]
= P/m*(1+r/n)[sup]nt[/sup]*(1-(1+r/n)[sup]-n(t+t/m)[/sup])/(1-(1+r/n)[sup]-nt/m[/sup])
P = 120000 (total invested)
m = 120 (120 payments of $1000 each)
r = 0.06 (%)
t = 10 (years)
n = 12 (monthly compounding)
gives a total of $165,698, or a 38.0% return. If you switch to yearly compounding (n=1), you get $164,124, or a 36.9% return.