How to Calculate APR Formula

When you borrow money, the lender discloses the interest rate on the loan. But that interest rate doesn't take into account charges related to the loan that are added onto your loan amount. The actual interest rate on your loan is higher than the interest rate disclosed by your lender. The APR, short for annual percentage rate, gives you a better idea of the effective interest rate on your loan. Lenders are legally required to disclose this rate to you.

Two Ways of Looking at Interest Rates

Interest Rate Before Costs

Assume you borrow $1,000 for one year, the nominal interest rate (the rate the lender usually advertises) is 8 percent per year and you make no principal repayments during the year, paying the loan off at the end of the year instead. The cost of the loan for this first year equals .08 times $1,000, or $80.

Interest Rate Including Most Costs

When you take out a loan, however, there are costs beyond the nominal interest rate, and these must be disclosed for the lender to comply with the federal Truth-in-Lending Act. According to the Nolo website, loan costs may include a loan origination fee, discount fee, points, mortgage broker fee, tax/flood service fees for the life of the loan, assumption fee, premiums for mandatory credit life or disability insurance, mandatory mortgage insurance premiums, lock or commitment fees, application fees, lender's attorney fees and settlement or closing fees.

In practice, few borrowers are hit with all of these charges. But most borrowers will have at least one and often several of them. These charges are added to your $1,000 loan, and from that point on you'll pay interest on both the principal amount and the added charges.

If the charges add another $60 to the loan, then the loan cost for the first year is $140 and the APR, which includes those costs in the calculation of interest, is 14 percent (140 divided by 1,000).

Determining APR

A relatively simple way of calculating the APR on a loan is to add both the fees and interest together, then divide by the amount financed. To make this formula workable when the loan period is more or less than one year, divide your result by the number of loan days given on your lending papers (usually called the term), then multiply by 365, the number of days in a year.

In most cases, however, you will be making periodic payments of interest and principal over the course of the loan. This complicates the calculation of APR, but fortunately there are many online APR calculators available -- Calculator Soup's APR Calculator, for example -- that ask you for some basic information about your loan, then calculate the APR for you.

Calculator Soup's APR Calculator asks you to enter the loan amount, the nominal interest rate, the compounding period of the loan (how often the lender recalculates the interest rate on the unpaid principal balance), the total number of payments, the frequency of payments and all fees and costs, including any prepaid amounts.

For example, say the nominal interest rate on a 30-year, $200,000 mortgage loan is 4.125 percent. Assume that the lender compounds the interest once monthly, that you make monthly payments and that the loan fees total $3,200 -- none of them prepayment charges. Plugging these figures into the calculator outputs an APR of 4.258 percent, not 4.125. The APR is a more realistic way of looking at the cost of a loan.