**Instructions:**

- Enter the Interest Rate (R), Compounding Frequency (m), and New Compounding Frequency (q).
- Click "Calculate" to calculate the equivalent periodic nominal rate.
- Your calculation history will be displayed below.
- Click "Clear" to reset the inputs and results.
- Click "Copy" to copy the result to the clipboard.

**Equivalent Periodic Nominal Rate:** -

**Calculation Details:**

**Explanation:** The equivalent periodic nominal rate is calculated using the formula:

**Equivalent Rate (r') = (1 + R/m)^(m/q) - 1 * q**

Where:

**R:**Interest Rate**m:**Compounding Frequency**q:**New Compounding Frequency**r':**Equivalent Periodic Nominal Rate

**Calculation History:**

The Equivalent Interest Rate Calculator is based on equivalent interest rates. Equivalent interest rates are interest rates with different compounding frequencies that result in the same future value for the same given present value and term. For example, if you invest $1,000 at 10.25% effective (compounded annually) for one year you will have the same future value ($1,102.50) as investing the $1,000 for one year at 10% compounded semi-annually.

## Formulae

The Equivalent Interest Rate Calculator uses the following formula to find equivalent interest rates:

### Formula

Given the periodic nominal rate r compounded m times per period, the equivalent periodic nominal rate i compounded q times per period is:

```
i = q ×[(1 + r/m)^m*q − 1]
```

where r = R/100 and i = I/100.

For example, if you have a loan at an annual rate of 4% that compounds monthly (m=12) however your payments are made quarterly (q=4) so your interest will be calculated quarterly. What is the equivalent annual rate that coincides with quarterly compounding?

```
4.0133% i = 4 ×[(1 + 0.04/12)^(12/4) − 1]
```

```
i = 0.040133
```

The effective annual interest rate remains the same.

## Benefits

The Equivalent Interest Rate Calculator offers several benefits, including:

### Accuracy

The Equivalent Interest Rate Calculator is a highly accurate tool that allows users to find equivalent interest rates with a high degree of precision. This eliminates the possibility of human error in calculations and ensures that interest rates are equivalent.

### Speed

The Equivalent Interest Rate Calculator is a fast tool that can find equivalent interest rates in seconds. This saves users time and allows them to focus on other important tasks.

### Convenience

The Equivalent Interest Rate Calculator is a convenient tool for any device with an internet connection. This makes it easy for users to find equivalent interest rates from anywhere, at any time.

## Interesting Facts

Here are some interesting facts about equivalent interest rates:

- Equivalent interest rates are used in many areas of finance, including loans, mortgages, and investments.
- Equivalent interest rates are interest rates with different compounding frequencies that result in the same future value for the same given present value and term.
- The Equivalent Interest Rate Calculator is a simple yet powerful tool that is easy to use and highly accurate.

**References**

Here are some scholarly references related to equivalent interest rates:

- Furey, Edward. “Equivalent Interest Rate Calculator.” CalculatorSoup, 2
- Elementary and Intermediate Algebra by Lynn Marecek and Mary Anne Anthony-Smith (2014)
- Basic Mathematics for College Students by Margaret L. Lial, Thomas H. Ratliff, Julie Beechner, and Julie O. Neill (2011)