Effective Annual Interest Rate Calculator

Introduction

Effective Annual Interest rate (EAR) is the total rate of return that a lender gets after considering the compounding effect, and the effective interest rate calculator will help you quickly and accurately determine it so that you can find out how much exactly you are paying to your lender.

The advertised interest rate from a bank or a lender is called the nominal rate. This rate does not take into consideration the effect of compounding.

The effective annual interest rate is the actual rate of return the borrower pays the lender, depending on the nominal interest rate and the number of compounding periods per year. It does not depend upon the amount invested.

How to use the Effective Annual Interest Rate (EAR) calculator?

Using the Effective Annual Interest Rate (EAR) calculator, you can find the Effective Annual Interest Rate by inputting the nominal interest rate and the compounding frequency.

The variables in the calculator are:

Nominal Interest Rate (N) The nominal interest rate or the stated interest rate in percentage.

Compounding Frequency (F) The frequency of compounding during the year.

Effective Annual Interest Rate (E) The effective annual interest rate after taking the effect of compounding into consideration.

What is the Effective Annual Interest Rate?

The effective annual interest rate (EAR) or the Annual Equivalent Rate (AER) is the real rate of return of an interest-paying investment when compounding effects are considered.

The more frequent the compounding, the higher the effective annual interest rate.

We can use the effective interest rates to compare the rates of return between multiple interest-paying securities.

How is the Effective Interest Rate Calculated?

The formula for Effective Annual Interest Rate (EAR) is given by the following formula

\text{Effective Annual Interest Rate} = {\bigg(1 + \dfrac{i}{k} \bigg)}^k - 1

Where

i = Nominal Interest Rate

k = Number of Compounding Periods per Year

Example

Now we know that an effective annual interest rate is useful in comparing two interest-paying securities on their true return, let’s look at an example.

Suppose, you have two loans, they both have the same principal of $10,000 and a nominal interest rate of 5%. But, one of the loans is compounded annually and the other loan is compounded quarterly.

Let’s calculate the effective annual interest rate of the first loan

\begin{aligned}\text{Effective Annual Interest Rate } &= {\bigg(1 + \dfrac{i}{k} \bigg)}^k - 1 \\[10pt]&= {\bigg(1 + \dfrac{5\%}{1} \bigg)}^1 - 1 \\[10pt]&= 5\% \\\end{aligned}

Let’s calculate the Effective Interest Rate of the second loan.

\begin{aligned}\text{Effective Annual Interest Rate } &= {\bigg(1 + \dfrac{i}{k} \bigg)}^k - 1 \\[10pt]&= {\bigg(1 + \dfrac{5\%}{4}\bigg)}^4 - 1 \\[10pt]&= 5.095\% \\\end{aligned}

As you can see the effective interest rate on the second loan is greater than the first because the second loan is being compounded more frequently.

Sometimes the stated interest rate and the effective interest rate can be very different, let’s look at an example.

Nominal Interest Rate	Semi-Annual	Quarterly	Monthly
1%	1.002%	1.004%	1.005%
2%	2.010%	2.015%	2.018%
3%	3.022%	3.034%	3.042%
4%	4.040%	4.060%	4.074%
5%	5.062%	5.095%	5.116%
6%	6.090%	6.136%	6.168%
7%	7.122%	7.186%	7.229%
8%	8.160%	8.243%	8.300%
9%	9.202%	9.308%	9.381%
10%	10.250%	10.381%	10.471%
15%	15.563%	15.865%	16.075%
20%	21.000%	21.551%	21.939%
25%	26.563%	27.443%	28.073%
30%	32.250%	33.547%	34.489%
35%	38.063%	39.868%	41.198%
40%	44.000%	46.410%	48.213%
45%	50.063%	53.179%	55.545%
50%	56.250%	60.181%	63.209%