Algebra
Exponential growth and decay
The value after t periods of multiplying by the same factor.
The Formula
A = P x (1 + r)^t
The value after t periods of multiplying by the same factor.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| A | Final value | units | The value after the periods have elapsed. |
| P | Starting value | units | The value at the beginning. |
| r | Rate | unitless | The rate per period, expressed as a fraction. |
| t | Periods | periods | The number of periods elapsed. |
What Each Symbol Means
Aunits
Final value
The value after the periods have elapsed.
Punits
Starting value
The value at the beginning.
runitless
Rate
The rate per period, expressed as a fraction.
tperiods
Periods
The number of periods elapsed.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate exponential 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 Exponential Growth, filed under Math. Every number the guide produces comes from substituting into this one line.