E-VAT System in Bangladesh: Meaning, Process & How It Works?

Effective Annual Interest Rate: Definition, Formula, and Example

The Effective Interest Rate (EIR), also known as the annual equivalent rate (AER) or annual equivalent percentage rate (APR), is a standardized interest rate that reflects the true cost or return on a financial product over a specified period. It accounts for compounding, making it a more accurate measure than the nominal interest rate.

Formula for Effective Interest Rate:

The formula for calculating the Effective Interest Rate is:

$EIR={(1+\frac{r}{n})}^n-1$

Where:

• $r$ is the nominal interest rate (expressed as a decimal),
• $n$ is the number of compounding periods per year.

Example:

Let's consider a loan with a nominal interest rate of 5% per annum compounded quarterly. We can calculate the Effective Interest Rate using the formula.

r = 0.05 \quad \text{(5% as a decimal)} $n=4\text{(compounded quarterly)}$

$EIR={(1+\frac{0.05}{4})}^4-1$

$EIR={(1+0.0125)}^4-1$

$EIR=(1.0125{)}^4-1$

$EIR\approx 0.05062$

In this example, the Effective Interest Rate is approximately 0.05062 or 5.062%. This means that if the loan is compounded quarterly at a nominal rate of 5%, the equivalent annual interest rate, accounting for compounding, is approximately 5.062%.

The Effective Interest Rate is crucial for comparing the true cost or return on different financial products, especially when they have different compounding frequencies. It provides a standardized measure that helps consumers and investors make more informed decisions.