I'll give a concrete example (couldn't find a similar question):

  • Let's say I have an amount of money M at time t = 0 (first month).
  • Every month, I get a given amount (let's say constant) of R
  • On my total amount of money for each month, I get a return of P percent per month.

What is the formula to know the final amount of money after t months?

  • Do you get R at the beginning of the month or at the end of the month? May 14, 2015 at 16:05
  • @DilipSarwate At end of the month
    – Symeof
    May 14, 2015 at 16:06
  • So how about trying to figure out, all by yourself, the formula for how much money you will have at the end of the first month, and the formula for how much money you will have at the beginning of the second month (t=1)? May 14, 2015 at 16:18
  • After one month it's: (M + R)*(1+P)^1 then it's ((M + R)*(1+P)^1) * (1+P)^2. It's recursive. Don't hesitate to risk being more helpful ;) My question is for t arbitrary, not t = 1...
    – Symeof
    May 14, 2015 at 16:21
  • Normally, formulas are here to accomodate EITHER no payment at t = 0 but payment at t = Final, OR payment at t = 0 but no payment at t = Final. Please choose one.
    – base64
    May 14, 2015 at 16:27

1 Answer 1


What's the future value of money given:

M = initial investment
R = additional monthly investment
P = interest rate earned per month
t = number of months

This is the result of 2 formulas. 1. How much is the initial investment worth at the end + 2. How much are the additional contributions worth at the end.

FutureValue[M] = M * (1+P)^t
FutureValue[R] = annuity calculation = R*((1+P)^t-1)/P)

So the future value of your initial investment with regular additions, all earning the same return monthly at the end of t months will be: M * (1+P)^t + R*((1+P)^t-1)/P)

  • How would you modify that to allow for an assumed inflation rate, to get an "in todsy's dollars" estimate of how much that will actually buy? Just subtract inflation rate from interest rate?
    – keshlam
    May 14, 2015 at 21:18
  • @keshlam I know that's a good ball park, but I'm not sure if it's 100% correct. I'd ask that as a new question and see what people say.
    – Alex B
    May 14, 2015 at 22:21

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