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Money guide

APR vs APY: What's the Difference and Which to Compare

APR is what a loan costs you per year, fees included. APY is what a savings account pays you per year, compounding included. Both are yearly percentages, but they are built differently and show up on different products. Here is what each one counts, the formulas, and which one to compare.

The difference in one sentence

APR stands for annual percentage rate and describes borrowing: the interest rate plus the fees charged with the loan, spread over a year. APY stands for annual percentage yield and describes saving: the interest you earn in a year once the interest itself starts earning interest. Loans, credit cards and mortgages come with an APR. Savings accounts, money market accounts and CDs come with an APY.

That split is not a marketing choice. Two federal rules decide it. Regulation Z, the Truth in Lending rules, defines the APR for credit. Regulation DD, the Truth in Savings rules, requires deposit account disclosures to state the annual percentage yield and the interest rate "using those terms". So a bank advertising a savings account must show you an APY, and a lender quoting a loan must show you an APR.

What the APR counts

The Consumer Financial Protection Bureau (CFPB) puts it simply: the interest rate is the cost of borrowing the money, and the APR is the interest rate plus the additional fees charged with the loan, such as origination charges. For a mortgage the APR includes points, mortgage broker fees and other charges. Because fees are added on top, a loan with fees has an APR above its interest rate. A loan with no fees has an APR equal to its rate.

For installment loans the APR is worked out with the actuarial method in appendix J of Regulation Z: find the rate per payment period that makes the payments worth exactly the amount you actually received, then multiply by the number of periods in a year. Take a loan of $10,000 at a 7% rate over 36 months with a $300 origination fee deducted from the proceeds. The payment is $308.77 a month, but you only received $9,700, so the APR is about 9.07%. The APR calculator does this for any loan, with fees paid upfront or rolled into the balance.

Credit cards use a simpler rule. Under 12 CFR 1026.14(b) the APR on open-end credit is each periodic rate multiplied by the number of periods in a year. A card with a daily periodic rate of 0.0658% has an APR of 0.0658 × 365, about 24%. That number does not include compounding, and it does not include annual fees. Card issuers usually calculate interest daily on your average daily balance (CFPB), and interest you do not pay is added to the balance, so carrying a balance for a whole year at a 24% APR costs about 27.1% of it. The credit card payoff calculator uses the same daily method to show how long a balance takes to clear.

What the APY counts

The APY answers one question: if you leave money in this account for a year, what percentage will it have grown by, counting the interest earned on earlier interest? The general formula from appendix A of Regulation DD is:

APY (Truth in Savings, appendix A)
APY = 100 × [(1 + Interest ÷ Principal)^(365 ÷ Days in term) − 1]

The rule's own example: an account pays US$61.68 of interest in a 365-day year on US$1,000, so the APY is 6.17%. When the rate is quoted as a nominal yearly rate compounded a fixed number of times a year, the same thing can be written as:

APY from a nominal rate
APY = (1 + rate ÷ n)^n − 1, where n is the number of compounding periods per year

A 4% rate compounded monthly gives (1 + 0.04 ÷ 12)^12 − 1 = 4.07%. Compounded daily it gives 4.08%. The more often interest is added, the higher the APY, but the gain flattens out quickly, which the table below shows. The compound interest calculator shows the balance year by year for any rate and compounding frequency, and the CD calculator turns a CD's rate and term into the amount at maturity.

APY for the same rate at different compounding

The nominal rate is in the first column. The other columns show what it becomes as an APY when interest is compounded yearly, monthly or daily. The last column is also what a credit card APR costs over a year of carrying the balance, because card interest accrues daily.

Nominal rateYearlyMonthlyDaily
1%1.00%1.00%1.01%
2%2.00%2.02%2.02%
3%3.00%3.04%3.05%
4%4.00%4.07%4.08%
5%5.00%5.12%5.13%
6%6.00%6.17%6.18%
8%8.00%8.30%8.33%
10%10.00%10.47%10.52%
15%15.00%16.08%16.18%
20%20.00%21.94%22.13%
25%25.00%28.07%28.39%
30%30.00%34.49%34.97%

At savings-account rates the gap is small: 4% becomes 4.07% monthly and 4.08% daily, a difference of a few cents a year per US$100. At credit-card rates it matters: a 25% APR works out to 28.4% a year when the interest compounds daily.

Which number to compare

Loan against loan: APR with APR

Two loans with the same interest rate are not the same loan if one charges a US$900 origination fee and the other charges nothing. The APR folds the fee in, so it is the number for comparing offers of the same kind and term. The loan calculator shows the payment from the interest rate; the APR calculator adds the fees and tells you which offer is cheaper over the full term.

Three cautions from the CFPB's mortgage guidance. Do not compare the APR of a fixed-rate mortgage with that of an adjustable-rate one, or two adjustable-rate loans with each other, because the APR of an ARM does not reflect the loan's maximum rate. The APR of a home equity line of credit does not include fees, while the APR of a closed-end loan does. And the APR depends on the full term: if you expect to sell or refinance after a few years, fees paid upfront weigh more than the APR suggests, so look at the total cost over the years you will actually keep the loan.

Savings against savings: APY with APY

Banks must disclose the APY, and because it already includes compounding, two accounts with the same APY pay the same over a year whatever their compounding schedule. An account advertising a 4.00% rate compounded daily and one advertising a 4.07% APY are the same deal. Enter the APY with yearly compounding, or the rate with its compounding frequency, into the savings goal calculator and the result is the same either way.

Loan against savings: convert first

Sometimes you want to know whether to pay down a card or put the money in savings. Then the two numbers need the same basis. Convert the card's APR to a yearly cost with daily compounding (24% becomes 27.1%) and compare it with the savings APY. If the card's effective rate is higher than the savings APY, and with the rates in the table it almost always is, every dollar on the card costs more than the same dollar earns in the account.

Common mix-ups

  • Reading a card's APR as the effective cost. The APR is the daily rate times 365. Carry the balance all year and the real cost is higher, by about 3 percentage points at a 24% APR.
  • Comparing an APY with an interest rate. The APY is always the larger of the two for the same account. Compare the two APYs, which the bank has to give you.
  • Ignoring fees because the rate is low. A low rate with a high origination fee can have a higher APR than a slightly higher rate with no fee, especially on a short loan, where the fee is spread over fewer payments.
  • Using the APR as the payment rate. The monthly payment comes from the interest rate, not the APR. The APR tells you what the loan costs; the rate tells you what you pay each month.
  • Trusting the APR of an ARM. The CFPB says it does not reflect the maximum interest rate of the loan, so it cannot tell you the worst case.

Frequently asked questions

Is APY always higher than APR?

For the same nominal rate, yes, as long as interest compounds more than once a year: 5% compounded monthly is a 5.12% APY, and compounded daily 5.13%. The two numbers are rarely quoted on the same product, though. Savings accounts and CDs show an APY, loans and credit cards show an APR. Compare APY with APY and APR with APR.

Does a credit card APR include compounding?

No. Under Regulation Z the APR on open-end credit is the periodic rate multiplied by the number of periods in a year, so a daily periodic rate times 365 or a monthly rate times 12. Interest is usually calculated daily on the average daily balance, and unpaid interest earns interest, so a 24% APR costs about 27.1% a year if you carry the balance all year.

Why is the APR on my mortgage higher than the interest rate?

The APR includes points, mortgage broker fees and other charges on top of the interest rate, so it is almost always higher. The CFPB warns that for an adjustable-rate mortgage the APR does not reflect the maximum rate of the loan, and that the APR of a home equity line of credit does not include fees, so compare like with like.

What is the APY formula?

The general formula in the Truth in Savings rules is APY = 100 × [(1 + Interest ÷ Principal)^(365 ÷ Days in term) − 1]. For a rate quoted as a nominal yearly rate r compounded n times a year, that works out to (1 + r ÷ n)^n − 1. Our compound interest calculator shows the result for any rate and compounding frequency.

Which number should I use in a calculator?

For savings, enter the interest rate with its compounding frequency, or enter the APY with yearly compounding; both give the same balance after a year. For a loan, the interest rate sets the payment; the APR tells you what the loan costs once fees are added, and is the number to compare between offers for the same type of loan.

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