how do you calculate APR?

Answer 1

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APR can include more than just the interest cost of a loan. On a mortgage, APR might include Private Mortgage Insurance, processing fees, and discount points. There are other fees and charges that may or may not be included in a given APR quote. Therefore, you need to look closely at each and every APR.
You can’t simply rely on an APR quote to evaluate a loan. You need to look at each and every charge and expense related to your prospective loan in order to judge whether or not you’re getting a good deal. In addition, look at the bigger picture – you need to know how long you’ll be using a loan to make the best decision. For example, one-time charges up front may drive up your actual cost on a loan – even though an APR calculation might assume those charges are spread out over a longer lifetime (and therefore the APR would look lower).


APR Example
APR seems really easy, but it’s amazing to watch the numbers (and your costs!) change with different scenarios.

Assume you will borrow $100, and the lender tells you you’ve got a 10% interest rate. If you use your $100 for a year, and then repay $110 at the end of the year, you actually did pay 10% APR. If, however, you repay the loan monthly in equal installments, you end up paying about 18% APR.

To test this, try the math yourself. In Microsoft Excel, use the RATE function and enter the following:

=RATE(12,-9.16,100)
The format is: RATE(nper,pmt,pv,fv,type,guess)

12 is the number of periods you pay on the loan (12 months or 1 year)
-9.16 is your payment ($100 loan + $10 interest = $110. $110/12 = 9.16)
100 is the present value of your loan (how much you’re borrowing today)

Answer 2

If interest is compounded monthly,

APR = (1+i)^12 - 1

where i is the monthly interest.