Effective Interest Rate Calculator

Formula

To calculate the Effective Interest Rate (ER):

\[ ER = \left(1 + \frac{i}{n}\right)^n - 1 \]

Where:

\(ER\) is the Effective Interest Rate
\(i\) is the nominal interest rate
\(n\) is the number of compounding periods per year

Effective Interest Rate Definition

The Effective Interest Rate (EIR) is a financial metric that measures the true cost of borrowing or the return on investment over a specified period. It is derived by accounting for interest compounding within a given time frame. Rather than solely considering the nominal interest rate, the EIR reflects the actual interest earned or paid, including any additional fees or charges.

Example Calculation 1

Let's assume the following values:

Nominal Interest Rate (\(i\)) = 5%
Number of Compounding Periods per Year (\(n\)) = 12

Using the formula:

\[ ER = \left(1 + \frac{0.05}{12}\right)^{12} - 1 \approx 0.0512 \text{ or } 5.12\% \]

The Effective Interest Rate is approximately 5.12%.

Example Calculation 2

Let's assume the following values:

Nominal Interest Rate (\(i\)) = 10%
Number of Compounding Periods per Year (\(n\)) = 4

Using the formula:

\[ ER = \left(1 + \frac{0.10}{4}\right)^{4} - 1 \approx 0.1038 \text{ or } 10.38\% \]

The Effective Interest Rate is approximately 10.38%.