Mortgages Analyzed

Effective Interest Rate

# Understanding EIR

Effective Interest Rate (EIR) is the nominal interest rate expressed in annual terms. Effective Interest Rate takes into account the differences in various payment streams by taking into account the interest rate and compounding terms.

EIR is also known as Effective Annual Rate, Effective Rate of Interest, Effective Annual Interest Rate, Annual Equivalent Rate, and the Effective Rate.

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# Formula for Calculating EIR

The formula for calculating Effective Interest Rate is:

EIR = [(1 + i)^c] - 1

The formula for calculating Effective Interest Rate in case of continuous compounding is:

EIR = er - 1

Where,

 EIR = Effective Interest Rate r = annual interest rate (expressed as % per year). Also known as nominal or coupon rate i = periodic interest rate (r/c) c = compounding periods per year

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# How EIR Works

Let’s assume that you took a loan of \$1,000 on Jan 1 at 12% compounded semi-annually.

On Jan 1, you started with a principal amount of \$10,000.

On June 30, you will accrue interest of \$600. (\$10,000 × 12% × 1/2). The new balance is \$10,600.

On Dec 31, you will accrue interest of \$636. (%10,600 x 12% × 1/2). The new balance is \$12,360.

At the end of the year you will pay \$12,360 in interest cost. The EIR is 13.36% because this is same as paying 12.36% per year in interest. In other words, 12% compounded semi-annually is same as EIR of 12.36% per annum.

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# Comparison of EIR to APR

Effective Interest Rate is interest rate stated in annualized terms after considering the compounding terms. It does not take into account the costs associated with a loan such as closing costs, commissions, and other costs. The Annual Percentage Rate (APR), on the other hand, is an annual rate that includes all the finance costs (various fees to obtain financing) and interest expense.

The table below summarizes the differences between the two rates.

Source :www.MortgagesAnalyzed.com
 Basis Effective   Interest Rate Annual Percentage Rate What it is EIR is the nominal interest rate expressed in annual terms. APR is the cost of loan expressed in annual terms. What it Includes EIR only considers takes into account the nominal interest rate and compounding. In addition to considering the nominal interest rate and compounding, it includes fees associated with a loan. These fees may include closing costs (example, credit report fee, application fee, and broker points), credit insurance fee, annual fee, account maintenance fee, and others. Legal Mandate The EIR is not defined by any regulation. The disclosure of EIR on a loan is not required by any regulation. The Truth in lending Act and the implementing Regulation Z provides the definition of APR and the method to calculate APR. Regulation Z also mandates the disclosure of APR on different type consumer loans, including mortgages. Purpose It is used to compare nominal rates between different loans. It is used to understand the cost of loan and to compare the annual cost between different loans. Example It helps compare a loan having 10% compounded quarterly to a loan having 9% compounded daily. It helps compare a loan having 10% interest rate with no closing costs to a loan having 9% interest rate with \$3,000 closing fee.
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# Examples

## Example 1: Monthly Compounding

Assume that Amit took a \$100,000 loan on Jan 1, 2000 for one year at an interest rate of 6% per annum compounded monthly. Principal and interest is payable at the end of the loan term.

Where,

 r = 6% i = 6%/12 = 0.005 c = 12

EIR = [(1 + 0.005)^12] – 1 = 6.16778%

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## Example 2: Continuous Compounding

Assume that Amit took a \$100,000 loan on Jan 1, 2000 for three years at an interest rate of 6% per annum compounded continuously. Principal and interest is payable at the end of the loan term.

Where,

 r = 6%

EIR = e^0.06 – 1 = 6.18365%

Source :www.MortgagesAnalyzed.com

# Calculators and Tools

1. Online EIR Calculator
2. EIR Calculator on a Spreadsheet
3. EIR Table. It shows the EIR for a given coupon rate and compounding periods.

Updated: Feb 18, 2013

Effective Interest Rate (EIR) is the nominal interest rate expressed in annual terms
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