Annual percentage rate, or APR, represents the cost of borrowing money for a home, car or other purchase. To the lender or investor, APR represents an annual return. While APR serves as a common representation of cost or return, it doesn't provide a complete picture of these costs. To understand the true cost or return associated with borrowing and lending, refer to the effective annual percentage rate, or EAR, which reflects the effects of compound interest.
Estimated Vs. True Cost
APR reflects the nominal rate of interest to be repaid or earned each year. If you borrow $1,000 for one year at an APR of 12 percent, the estimated interest can be calculated as (1,000 times 0.12), or $120. In most cases, however, you will actually pay slightly more than than $120 in interest.
To calculate the true interest you'll pay, you must consider the EAR. EAR helps you determine not only the amount of interest you pay on your principal, but also the amount of interest you'll pay on the interest owed with each payment. A $1,000 loan with an APR of 12 percent actually results in an EAR of 12.55 annually. This means you will pay a total of $125.50 in interest over the year.
Lenders naturally want to make the interest rate on a loan look as low as possible so that people will be more likely to buy. In most cases, car dealers, creditors and other lenders advertise the APR because it has a lower value than EAR. This serves as a technique for skewing the views of buyers, or taking advantage of the fact that many people know little about compound interest.
Banks and other financial institutions, on the other hand, use EAR to make the interest look as high as possible. This encourages people to invest, or open a savings account. In investment applications, EAR is often listed as annual percentage yield, or APY, though these two terms mean the same thing.
Both APR and EAR can serve as effective tools for comparing interest rates on loans on investment options. The key is to make sure you are comparing APR to APR, or EAR to EAR. APR figures also ignore any loan fees, so consumers should ask about these fees when using APR. While EAR figures may include loan fees, this isn't always the case depending on how the loan is structured, so buyers should also inquire about fees when using EAR figures.
How to Calculate Interest
Calculating interest using APR is relatively simple. Multiply the amount of the original loan by the APR, expressed as a decimal. This gives you the amount of total annual interest. To determine how much interest you'll pay each month, divide the total annual interest amount by 12.
EAR calculations are slightly more complex, and require the use of the formula: (1+r/n)^nth power-1. In this formula, r represents the APR and n represents the number of times the interest is compounded each year. For example, a car loan with monthly payments would generally be compounded 12 times each year. Some loans are compounded quarterly or even daily. Using this formula, a loan with an APR of 6 percent would have an EAR of 6.183 percent if compounded daily, 6.17 percent if compounded monthly and 6.14 percent if compounded quarterly. By multiplying these EAR numbers by the amount of the loan, you can determine the true cost of the loan.
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