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Annual percentage rate

An annual percentage rate, or APR, is the quoted annual rate of interest paid on a deposit or charged on a loan.

Expanded Definition

APR is one of those terms that you should pay attention to when you apply for a credit card or other loan or when you deposit your money in the bank in a savings account or certificate of deposit.

Oh, you better also pay attention to how often the interest is compounded.

Interest, of course, is the amount of money you pay for the right to borrow it (as in a credit card or mortgage) or the amount the bank pays you when they borrow your deposit. What's usually quoted is the APR. For instance, if you have a credit card with an APR of 18%, then you will be paying 18% per year on the money you borrow. If you deposit money into a CD with an APR of 5%, then you will be paid 5% per year.

But, it's a bit more complicated than that. (Isn't it always.) You see, the interest amount you actually end up paying or receiving depends on how often the interest is compounded. That is, how often the interest is added to the principal so that interest can be charged or paid on that interest. The more often this happens, the higher the actual interest charged / paid becomes. That actual interest rate is called the annual percentage yield or APY. And APY is always higher than APR.

An Example of APR vs APY

If you sign up for a credit card with a 18.25% APR, and you charge $1025 to it in the first month, you generally can avoid paying any interest on that debt if you pay the full balance at the first payment due date. However, if you choose to make the minimum payment, let's say $25, you will be charged interest on the rest.

Now, you might think that it would be 18.25% / 12 = 1.5208% or $15.21. But you'd be wrong. See, the interest on a credit card is almost always compounded daily. And this is how it's calculated:

18.25% / 365 = 0.05000% per day This rate is compounded daily.
$1000 * (1.0005)^30 = $1015.11 (For a 30-day payment period.)

So, for the first month, you were charged $15.11.

But, if you didn't make any further payments and we ignore late fees and other stuff credit card companies like to tack on, just to see what the total interest would be, we could compound that 0.05% for a full year:

$1000 * (1.0005)^365 = $1,200.16.

Whoa! That's $200.16 in interest, and is quite a bit more than the $182.50 the APR suggests would be the amount extra ($1000 * 18.25%). That extra $17.66 happens because of the daily compounding

In this case, the APR is 18.25%, while the APY is 20.016%. Quite a difference.

Practical Application

When evaluating credit card offers, or any other loan offer, pay attention to both numbers, the APR and the APY. The bigger the difference between them, the more often the interest is compounded. While that works for you on a savings account, it works against you on a credit card.

Also, remember that a low APR may be introductory oonly, meaning it will be raised to a higher APR (and APY) after some time has gone by. Also note that the APR does not include such things as late payment penalties or other fees.

These calculations may seem complex, likewise when calculating a mortgage payment from a mortgage APR, and more complex still with an interest-only mortgage or an adjustable-rate mortgage. However, doing these calculations are an absolutely essential part of applying for a loan. Too many people not doing so helped produce the credit crunch.

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