APR Calculator

The annual percentage rate (APR) expresses the yearly cost of borrowing, including certain fees, as a single rate. The interest rate on its own tells you how the balance grows; the APR also accounts for money you pay to get the loan. If two lenders quote the same 6% rate but one charges $2,500 in fees, the second loan's APR is higher, and that difference is what the calculators above measure.

Under the federal Truth in Lending Act, lenders must disclose the APR before you sign so that offers can be compared on equal terms. For a mortgage it appears on the Loan Estimate and the Closing Disclosure. Which costs count as finance charges is defined by regulation. Fees that only exist because you are borrowing are generally included; costs you would pay in a cash purchase, such as most title, appraisal and recording fees on a mortgage, are generally left out.

The calculator assumes upfront fees are paid at closing or subtracted from the funds you receive, while loaned fees are added to the balance and repaid with interest. In both cases you end up with less usable cash for the same payments, which raises the effective rate. The table lists charges commonly counted in a mortgage APR and costs that usually are not.

Limitations of the APR

APR is a useful comparison tool but not a perfect one. It spreads upfront fees over the full term, so it understates the true cost if you sell or refinance early: $3,000 of fees on a loan you keep for three years costs far more per year than on one you keep for thirty. A loan with low fees and a slightly higher rate can be cheaper for a short holding period even when its APR is higher.

APR also leaves out costs that are excluded by regulation, so two loans with the same APR can still have different closing costs. For adjustable-rate loans, the APR is based on assumptions about future rates. Always read the full cost breakdown alongside the headline rate.

Types of APRs

Fixed APRs. A fixed APR does not change with market rates. Installment loans such as most mortgages, auto loans and personal loans usually carry fixed rates, giving predictable payments for the whole term. On credit cards, a so-called fixed APR is less permanent: the issuer can still raise it on new purchases after giving 45 days' notice under the Credit CARD Act.

Variable APRs. A variable APR moves with an index, most often the prime rate, plus a margin set by the lender. Most credit cards, home equity lines of credit and many private student loans are variable. When the Federal Reserve raises its target rate, the prime rate typically rises within days and variable APRs follow, increasing interest charges on existing balances.

Credit cards often apply different APRs to different kinds of balances on the same account. The purchase APR covers everyday spending. The balance transfer APR applies to debt moved from another card and is often a temporary promotional rate, sometimes 0%, for a set number of months. The cash advance APR applies to cash withdrawals and is usually higher, with interest starting immediately rather than after a grace period. A penalty APR, which can approach 30%, may be imposed after a payment that is more than 60 days late.

An introductory APR is a low or zero rate offered for the first months of a new account. When it ends, the regular rate applies to any remaining balance, so plan to clear the balance before then.

APR vs. APY

APR and APY both describe a yearly rate but answer different questions. APR, used for loans, is the periodic rate multiplied by the number of periods in a year and ignores compounding. APY, the annual percentage yield, includes the effect of compounding and shows the rate actually earned or paid over a full year. Banks quote APY on savings accounts and CDs because it is the larger and more flattering figure; lenders quote APR.

The difference grows with the rate and the compounding frequency. A credit card with an 18% APR that compounds monthly charges 1.5% a month, which over a year works out to an effective rate of about 19.56%. A 6% APR compounded monthly is an APY of 6.17%.

For example, $100 borrowed at a 10% APR compounded monthly grows to $110.47 after a year if nothing is repaid, an APY of 10.47%, while simple annual interest at 10% would give $110.00.

To convert in the other direction, use APR = n × [(1 + APY)^(1/n) − 1]. A savings account advertising a 5.00% APY with daily compounding pays a nominal rate of about 4.88%. When comparing products, make sure both rates are on the same basis: compare APR with APR for loans and APY with APY for deposits.

APY = (1 + APR ÷ n)ⁿ − 1

APR

nominal annual rate, as a decimal

n

number of compounding periods per year (12 for monthly)

The real APR itself has no closed form: it is the rate r at which the present value of all payments equals the loan amount minus upfront fees, found by numerical search and then multiplied by the number of payments per year.

Frequently asked questions

Sources

• CFPB – What is the difference between a mortgage interest rate and an APR?
• CFPB – Regulation Z (Truth in Lending)
• Board of Governors of the Federal Reserve System