Investing
Monthly rate from an annual rate
An annual return is converted by taking its twelfth root rather than by dividing by twelve, because the compounding has to compound rather than merely accumulate.
The Formula
monthly rate = (1 + annual rate)^(1/12) - 1
An annual return is converted by taking its twelfth root rather than by dividing by twelve, because the compounding has to compound rather than merely accumulate.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| r_a | Annual return | percent | The yearly rate of return. |
| r_m | Monthly return | percent | The equivalent rate per month. |
What Each Symbol Means
r_apercent
Annual return
The yearly rate of return.
r_mpercent
Monthly return
The equivalent rate per month.
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.