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:
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 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.
The Annual Percentage Rate (APR) represents the total borrowing cost, expressed as a yearly rate, relative to the initial loan amount. The Effective Interest Rate (EIR) is the rate that reflects the true cost of borrowing and takes into account total charges.
An interest rate takes two forms: nominal interest rate and effective interest rate. The nominal interest rate does not take into account the compounding period. The effective interest rate does take the compounding period into account and thus is a more accurate measure of interest charges.
Interest rates are influenced by factors such as your credit score, the lender you work with, inflation and the broader economy. When comparing loan offers, it's best to compare APRs to get a fuller picture of the true cost of the financing.
Effective Interest Rate (EIR) - What Your Loan Actually Costs. The true cost of your loan is known as the Effective Interest Rate (EIR) which may be higher than the advertised rate because of the way interest is calculated.
Here are the formula and calculations: Effective annual interest rate = (1 + (nominal rate ÷ number of compounding periods))(numberofcompoundingperiods) – 1. Investment A = (1 + (10% ÷ 12 ))12 – 1.
EIR equation: EIR = ( 1 + nominal rate ) n − 1 Where n represents the number of compounding periods per year. 3. Calculating the Interest Income or Expense: The quantum of interest income or expense for a given period is derived using the EIR.
For example, nominal interest rates indicate what we'd be charged for a loan, but the real interest rate can help us decide whether or not the loan is too costly for our budgets. As far as purchasing power goes, a real interest rate that's positive is always good, unless the inflation rate is greater.
An APR tends to be higher than a loan's nominal interest rate. That's because the nominal interest rate doesn't account for any other expense accrued by the borrower. The nominal rate may be lower on your mortgage if you don't account for closing costs, insurance, and origination fees.
First, let's define the meaning of EIR: Effective Interest Rate (EIR) is the total cost of borrowing a loan, expressed as a percentage of the amount borrowed. Unlike the annual interest rate, EIR takes into account the impact of compounding.
The APR reflects the interest rate, any points, mortgage broker fees, and other charges that you pay to get the loan. For that reason, your APR is usually higher than your interest rate.
The lower the APR, generally the better it is for the cardholder. Though we recommend against carrying a credit card balance, advancing cash or doing anything else to incur interest fees, a relatively “good” APR can reduce the impact in the event of the unexpected.
The comparison rate gives you a better indication of the true cost of the loan and is generally higher than the interest rate, because it takes into account additional costs, such as: Application fees. Establishment fees. Ongoing account keeping fees or charges.
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.
The effective interest rate (EIR), effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the percentage of interest on a loan or financial product if compound interest accumulates in periods different than a year.
The 'nominal' rate refers to the interest you'd earn over the year if you withdraw that interest from the account every month. The annual 'effective' rate reflects the amount paid over the year if the interest is added to the account balance every month.
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.
The main difference between APR and EAR is that APR is based on simple interest, while EAR takes compound interest into account. APR is most useful for evaluating mortgage and auto loans, while EAR (or APY) is most effective for evaluating frequently compounding loans such as credit cards.
APR represents the total yearly cost of borrowing money, expressed as a percentage, and includes the interest you pay on a loan. APY refers to the total amount of money you earn on a savings account or other investment, taking into account compound interest.
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