Annual percentage rate, or APR, goes a step beyond simple interest by telling you the true cost of borrowing money. For example, the APR you receive when you buy a house takes into account the fees you pay to originate the loan, as well as the interest you'll pay. However, APR doesn't include the effects of compound interest.
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On the other hand, effective annual percentage rate, also known as EAR, EAPR, or annual percentage yield (APY), takes the effects of compound interest into account.
Annual percentage rate
There are several possible definitions of APR, but we'll use the term to represent the nominal APR. This simply refers to the periodic interest rate for a loan, multiplied by the number of payment periods each year. For example, if a credit card charges 1% interest per month, multiplying it by 12 gives a nominal APR of 12% per year. In the United States, calculation of APR is dictated by the Truth in Lending Act. Under these guidelines, APR includes any fees that are incorporated into the loan's principal balance. For example, if you apply for a mortgage, you may see an interest rate of 4% and an APR of 4.1% listed. The reason for the higher APR is likely to be the loan's origination fee.
Effective annual percentage rate (annual percentage yield)
Effective APR takes into account the effects of compound interest, and is useful for evaluating loans that compound interest at regular intervals, such as monthly or daily. As I mentioned in the previous section, the nominal APR for a credit card that charges 1% interest per month is 12%. However, each month, that interest gets tacked on to your balance, and you'll pay interest on any unpaid interest charge during the following month. In fact, most credit cards compound interest daily
Mathematically, effective APR for a loan can be calculated as follows:
So a 1% monthly interest charge on a credit card has an effective APR of:
Going further, since a nominal APR of 12% corresponds to a daily interest rate of about 0.0328%, we can calculate the effective APR if this credit card computes interest daily as:
The main takeaway from this example is that the more frequently interest is compounded, the higher the effective APR will be. And, since it is beneficial to a bank's profits to compound interest frequently (daily) on credit cards and other loans, that's exactly what most of them do.
Understanding how effective APR works can be especially useful when evaluating the cost of short-term loans. Let's say that a friend offers to loan you $1,000 for one month if you'll pay him back $1,050, or 5% interest. However, when you extrapolate that interest rate over a year, you'll find that you're actually paying an effective APR of nearly 80%. All of a sudden, this loan looks a little more expensive.
For investors, EAR or APY can help you analyze your actual return on an investment like a CD. Let's say that you buy a one-year CD with a 3% annual interest rate, compounded monthly (0.25% per month). Using our compounding formula, we can calculate the effective APR to be 3.04%, or slightly higher than the advertised rate.
The bottom line
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.
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