Retirement
Future value of a 401(k) with match
The first term compounds the opening balance; the second is the future value of a level annual deposit of your contribution plus the match.
The Formula
FV = B(1+r)^t + (C + M) x [((1+r)^t - 1) / r]
The first term compounds the opening balance; the second is the future value of a level annual deposit of your contribution plus the match.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| B | Opening balance | currency | Balance already saved. |
| C | Annual contribution | currency | Your yearly deposit. |
| M | Employer match | currency | Employer money added each year. |
| r | Annual return | rate | Assumed growth rate. |
| t | Years | count | Years until retirement. |
What Each Symbol Means
Bcurrency
Opening balance
Balance already saved.
Ccurrency
Annual contribution
Your yearly deposit.
Mcurrency
Employer match
Employer money added each year.
rrate
Annual return
Assumed growth rate.
tcount
Years
Years until retirement.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate 401(k) growth 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 Calculate 401(k) Growth, filed under Finance. Every number the guide produces comes from substituting into this one line.