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Periodic Return to Compound Annual Rate Calculator

Annualize a periodic return using repeated compounding.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Edit a calculated value to solve backwards, or lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

A return of 1% repeated monthly compounds to approximately 12.6825% over twelve months. Simply multiplying by twelve would give a different measure.

Annualized return = (1 + periodic return)^periods per year − 1

Worked example

Enter these known values and leave the other values blank.

Period
Monthly
Period rate
1 %
Annualized rate of return
12.683 %

Assumptions and limitations

  • No. It assumes the same return repeats with reinvestment. Daily and weekly modes use 365 and 52 periods respectively. Use economically meaningful returns of at least −100%; fees, taxes and changing returns are not modeled.
  • Use consistent periods, currency and accounting definitions. The result follows the stated formula and the figures you supply.

Common questions

Does annualizing a short-period return predict the next year?

No. It assumes the same return repeats with reinvestment. Daily and weekly modes use 365 and 52 periods respectively. Use economically meaningful returns of at least −100%; fees, taxes and changing returns are not modeled.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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