Investing
Total income over a horizon with growth
With the dividend growing each year, the income stream is a growing annuity. Summing it gives the closed form shown, and the result grows quickly with the horizon.
The Formula
total = income x ((1+g)^n - 1) / g
With the dividend growing each year, the income stream is a growing annuity. Summing it gives the closed form shown, and the result grows quickly with the horizon.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| I | Year-one income | currency | The dividend income in the first year. |
| g | Growth rate | percent | Assumed annual growth in the dividend. |
| n | Years | years | How many years income is counted for. |
| T | Total income | currency | The sum of every year's payment. |
What Each Symbol Means
Icurrency
Year-one income
The dividend income in the first year.
gpercent
Growth rate
Assumed annual growth in the dividend.
nyears
Years
How many years income is counted for.
Tcurrency
Total income
The sum of every year's payment.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate dividend income 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 Dividend Income, filed under Finance. Every number the guide produces comes from substituting into this one line.