# EAR Calculator

## Make Smart Investments Decisions With the EAR Calculator

**Table of Contents**

- What Is the Effective Annual Rate (EAR)?
- What Is the Compounding Period?
- How To Calculate the Effective Interest Rate?
- The EAR Formula
- Example #1: Annually Compounded Interest
- Example #2: Quarterly Compounded Interest
- Example #3: Monthly Compounded Interest
- The Importance of the Effective Annual Rate

The Effective Annual Rate calculator is a great tool. It enables you to compare the return rates of your investment, or effective costs of your loan when compounding intervals vary. Whether monthly, yearly, or quarterly compounding, this tool calculates the EAR for you.

Below, you’ll find everything you need to know about the Effective Annual Rate (EAR). you’ll also get to understand why it’s important and what the formula to calculate it is.

## What Is the Effective Annual Rate (EAR)?

Simply put, the Effective Annual Rate is the “actual” interest rate you get on an investment or you pay on a loan. This means that it’s the real percentage of interest, after calculating and compounding it, over a certain period.

Usually, the Effective Annual Rate is higher than the nominal rate, which is the basic interest rate that’s often stated by the financial institution.

The EAR also varies according to the compounding period of your choice.

### What Is the Compounding Period?

This compounding period is the time after which the interest is added to the primary amount of the loan or investment. It could be monthly, quarterly, or annually.

Consequently, the number of compounding periods is 1 for annual interest, 4 for quarter interest, and 12 for monthly interest. The higher the compounding number, the more the Effective Annual Rate increases.

## How To Calculate the Effective Interest Rate?

When comparing the effective rate to the nominal rate, you find that the latter is lower. That’s because the nominal rate represents the yearly percentage, with a disregard for compounding. So, how to calculate the Effective Interest Rate?

Basically, the Effective Annual Rate of an annually compounded investment is still the same value as the nominal rate. That’s because, in this case, compounding has the value of one.

On the other hand, when it comes to quarterly or monthly compounded investments, there’s a simple formula to calculate the EAR.

### The EAR Formula

The EAR formula is quite straightforward. Here’s how it goes:

**EAR = ((1+ nominal interest rate / number of compounding periods) ^ number of compounding periods) - 1**

#### Example #1: Annually Compounded Interest

A given bank offers investment certificates with a nominal annual interest rate of 8%. So, a client decides to invest an amount of $10,000 for one year. This client chooses the option of annually compounded interest.

In this case, the number of compounding periods is one. Therefore, you calculate the EAR as follows:

**EAR = ((1+0.08/1)^1) - 1 = 8%**

This explains why the EAR is the same as the nominal rate for a year-long annually compounded interest.

#### Example #2: Quarterly Compounded Interest

When it comes to quarterly compounded interest, the number of compounding periods increases to four. That’s because four is the number of quarters in one year. Therefore, the EAR increases to:

**EAR = ((1+0.08/4)^4) - 1 = 8.243%**

#### Example #3: Monthly Compounded Interest

Similarly, the number of compounding periods in a monthly compounded interest rate is 12. So, the EAR becomes:

**EAR = ((1+0.08/12)^12) - 1 = 8.3%**

## The Importance of the Effective Annual Rate

Knowing the Effective Interest Rate is rather crucial when choosing to invest a certain amount of money or applying for a loan.

It helps you get an overview of the actual return on investment you get when compounding differs. Moreover, it enables you to calculate the expenses on a loan you pay with different compounding intervals.

Additionally, calculating the EAR allows you to compare different investment types, such as certificates of deposits (CD) with different compounding periods or various investing instruments.

This way you become fully aware of the effects resulting from the choices you make, for example, CD, which is a type of deposit account vs. a savings account.

EAR is as important for businesses as it is for individuals. That’s because the cost of debt has a direct impact on the business’s profitability. In other words, the higher the interest expense is, the lower the company’s net income becomes.

### Authors

Created by **Lucas Krysiak** on 2022-11-17 16:20:38 | Last review by **Mike Kozminsky** on 2022-11-29 18:05:16