 # Interest Rates 101: APR vs. EIR

Understanding the difference between two common ways of calculating interest is important for protecting client interests Pricing transparency is at the core of the Smart Campaign’s Client Protection Principles. But interest rates are often difficult to understand, calculate, and compare due to variables including associated fees, commissions, savings requirements, and different methods of calculating interest.

In keeping with the Smart Campaign’s goal of ensuring that pricing, terms, and conditions of financial products are transparent and adequately disclosed in a form understandable to clients, this is the first in a series of posts providing some fundamental concepts — including a review of some common practices and definitions of basic terms — to keep in mind.

### Annual Percentage Rate and Effective Interest Rate

The most common and comparable interest rate is the APR (annual percentage rate), also called nominal APR, an annualized rate which does not include compounding. The United States Truth in Lending Act requires disclosure using the APR, and it is used as a standard rate in many other countries.

The APR can be calculated by multiplying the periodic interest rate (say 2 percent per month) times the number of periods per year (in this case 12). Where n equals the number of periods per year and i equals the periodic (in this case, monthly) interest rate, then APR can be calculated as:

APR = i * n; or, using our example: 2% * 12 = 24%

The EIR, or effective interest rate, also known as effective APR, effective annual rate (EAR), or annual equivalent rate (AER), takes into account the effect of compounding.

EIR is the standard method of interest calculation in the European Union, and interest rates on all consumer loans in the EU must be disclosed in this format.

The EIR calculation is used in cases where interest is compounded, i.e. when interest is charged upon interest. Compound interest is used to calculate payments on credit card debt, where interest can be charged on existing interest, or other types of revolving credit facilities where outstanding interest not paid on time is added to the amount of principal owed and interest is subsequently charged on the new total. Because the EIR takes compounding into account it will always be greater than APR for a given loan, provided that the compounding occurs more frequently than once per year.
In microfinance, EIR is a less useful calculation than APR when calculating the cash cost of borrowing (it overstates cash costs for traditional loans with constant installments). The EIR, however, assigns a time value to money, regardless of whether it is charged in cash, and is therefore conceptually more complete.

Where n equals the number of compounding periods per year and i equals the periodic interest rate, EIR can be calculated as:

EIR = (1+i)n – 1

Using our previous example, where the quoted interest rate is 2 percent per month:

EIR = (1+.02)12 – 1 = .268242 or 26.8%

Note that the EIR is higher than the APR calculated using the same periodic interest rate and number of periods per year because the EIR takes into account the effect of compounding.

EIR can be calculated using the above formula with a financial calculator (or any calculator which has an exponent (yx) function) or using a basic spreadsheet program like Excel.

The following table illustrates the amortization of a \$1,000 loan over 6 months using both approaches: Next to come, Flat vs. declining balance rates