Investing
Future value of a stream of contributions
This is the ordinary annuity future-value formula. Each payment compounds for the months remaining after it is made, and the sum of all those factors collapses into a single closed form.
The Formula
FV = A x ((1+r)^n - 1) / r
This is the ordinary annuity future-value formula. Each payment compounds for the months remaining after it is made, and the sum of all those factors collapses into a single closed form.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| A | Contribution | currency | The amount invested each period. |
| r | Periodic return | percent | The return per period, not per year. |
| n | Periods | months | How many contributions are made. |
| FV | Future value | currency | What the stream of contributions is worth. |
What Each Symbol Means
Acurrency
Contribution
The amount invested each period.
rpercent
Periodic return
The return per period, not per year.
nmonths
Periods
How many contributions are made.
FVcurrency
Future value
What the stream of contributions is worth.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to dollar-cost average page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Dollar-Cost Average, filed under Finance. Every number the guide produces comes from substituting into this one line.