\[r_2 = \left(1+\frac{r_1}{n_1}\right)^{\frac{n_1}{n_2}} - 1\]
Variables
r2equivalent interest rate
r1original interest rate
n1original compounding periods
n2target compounding periods
Description
What is this formula?
The equivalent interest rate conversion formula calculates an interest rate with a different compounding frequency that produces the same effective return.
When to use it
Use this formula when comparing financial products or converting rates between different compounding periods.
Example
If a monthly interest rate system uses a nominal annual rate of 12% compounded monthly and you want the equivalent quarterly rate:
r2 = (1 + 0.12/12)^(12/4) - 1 ≈ 0.0303
The equivalent quarterly interest rate is approximately 3.03%.
Applications
Banking, investment comparison, loan analysis, and financial mathematics.