APR vs APY: What's the Difference?
By the Calculator.hair team · Updated · 6 min read
Short answer
APR (annual percentage rate) is a yearly rate that does not include compounding, and on loans it can include certain fees. APY (annual percentage yield) includes compounding, so it shows what you actually earn in a year. The formula is APY = (1 + r/n)^n - 1. At 4% compounded monthly, APY is 4.07%. Loans usually quote APR and savings accounts quote APY.
Key takeaways
- APY is always equal to or higher than the same rate quoted as APR, because it includes interest on interest.
- Effective annual rate = (1 + r/n)^n - 1, where r is the nominal rate and n is the compounding periods per year.
- On a loan, APR adds fees to the interest rate: a $20,000, 5-year loan at 7% with a $600 fee has an APR of 8.286%.
- Compare accounts by APY and compare loans by APR, using the same term and fee assumptions.
What is the difference between APR and APY?
APR states the yearly cost of borrowing without compounding; APY states the yearly return including compounding. A nominal rate is the stated yearly rate before compounding, and compounding means interest is added to the balance so that it earns interest too.
The terms come from two different federal disclosure laws. The Truth in Lending Act and its Regulation Z require lenders to disclose APR on credit. The Truth in Savings Act and its Regulation DD require banks and credit unions to disclose APY on deposit accounts. That is why a credit card ad shows APR and a savings ad shows APY.
| APR | APY | |
|---|---|---|
| Full name | Annual percentage rate | Annual percentage yield |
| Includes compounding? | No | Yes |
| Includes fees? | Often on loans; usually not a card's annual fee | No |
| Usually quoted on | Loans, mortgages, credit cards | Savings accounts, CDs, money market accounts |
| Which is better? | Lower, when you borrow | Higher, when you save |
What is the effective annual interest rate formula?
The effective annual rate (EAR) is (1 + r/n)^n - 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For deposits, EAR and APY describe the same idea.
Worked example: a 4% nominal rate compounded monthly gives (1 + 0.04/12)^12 - 1 = 0.04074, or 4.074%. With continuous compounding, the formula becomes e^r - 1, which at 4% is 4.081%.
To go the other way, from APY to the nominal rate, use r = n × ((1 + APY)^(1/n) - 1). A 5% APY with monthly compounding equals a nominal rate of 4.889%.
- APY = (1 + r/n)^n - 1
- Nominal rate from APY: r = n × ((1 + APY)^(1/n) - 1)
- Continuous compounding: APY = e^r - 1
- Daily periodic rate = APR ÷ 365
- Monthly periodic rate = APR ÷ 12
How do you convert APR to APY?
Divide the APR by the number of compounding periods, add 1, raise to the number of periods and subtract 1. The more often interest compounds and the higher the rate, the bigger the gap between the two numbers.
At savings rates the gap is small: 4% becomes 4.074% with monthly compounding. At credit card rates it is much wider: 24% becomes 27.115% with daily compounding. All figures below use the formula in our calculators.
| Nominal rate (APR) | Compounded quarterly | Compounded monthly | Compounded daily |
|---|---|---|---|
| 1% | 1.004% | 1.005% | 1.005% |
| 2% | 2.015% | 2.018% | 2.020% |
| 3% | 3.034% | 3.042% | 3.045% |
| 4% | 4.060% | 4.074% | 4.081% |
| 5% | 5.095% | 5.116% | 5.127% |
| 6% | 6.136% | 6.168% | 6.183% |
| 10% | 10.381% | 10.471% | 10.516% |
| 18% | 19.252% | 19.562% | 19.716% |
| 20% | 21.551% | 21.939% | 22.134% |
| 24% | 26.248% | 26.824% | 27.115% |
| 30% | 33.547% | 34.489% | 34.969% |
How does compounding change what you earn on savings?
More frequent compounding earns slightly more, and the difference grows with time. In our savings calculator, $10,000 at a 4% nominal rate with no further deposits and no tax earns $400.00 in one year with annual compounding, $407.42 with monthly and $408.08 with daily.
Over 10 years the same deposit grows to $14,802.44, $14,908.33 and $14,917.92. The rate itself matters far more than compounding frequency, so a higher APY is the number to look for. For the full math over longer periods, see the compound interest formula.
APY also makes quotes comparable. An account with a 3.95% rate compounded monthly has an APY of 4.022%, so it pays more than an account advertising 4.00% APY, despite the lower headline rate.
| Compounding on $10,000 at 4% | APY | After 1 year | After 10 years |
|---|---|---|---|
| Annually | 4.000% | $10,400.00 | $14,802.44 |
| Monthly | 4.074% | $10,407.42 | $14,908.33 |
| Daily | 4.081% | $10,408.08 | $14,917.92 |
Why is a loan's APR higher than its interest rate?
A loan's APR is higher than its interest rate because APR counts certain fees as part of the cost of borrowing, spread over the loan's term. The interest rate alone sets your monthly payment, while the APR shows the cost once fees are included.
Worked example: a $20,000 loan for 5 years at 7% has a monthly payment of $396.02. If the lender charges a $600 upfront fee, you receive $19,400 but still repay $23,761.44 over 60 payments. Our APR calculator solves for the rate that matches those cash flows: 8.286%. That is well above the 7% quoted rate, and short loans show a bigger gap because the fee is spread over fewer years.
If you know only the balance and payment, the interest rate calculator works backward: a $32,000 loan paid at $960 a month for 3 years has a rate of 5.065%, with $2,560 of total interest. For home loans, compare the note rate and APR with how to calculate a mortgage payment.
What does APR mean on a credit card?
On a credit card, APR is the yearly interest rate, and many issuers apply it daily using a daily periodic rate of APR ÷ 365. A 24% APR is about 0.0658% a day.
Because unpaid daily interest joins the balance, a 24% APR compounded daily has an effective annual rate of 27.115%. A $1,000 balance with no payments and no new charges would grow to about $1,271 in a year, not $1,240. Cards can carry several APRs, such as one for purchases and another for cash advances, and an annual fee is usually charged separately rather than built into the purchase APR.
If you pay the statement balance in full by the due date, a card's grace period usually means you pay no purchase interest at all. If you carry a balance, see how to pay off credit card debt.
What is the annual interest rate formula?
For simple interest, the annual rate is interest ÷ (principal × years). Earning $400 on $10,000 in one year is $400 ÷ ($10,000 × 1) = 4%.
To annualize a periodic rate, multiply it by the number of periods to get the nominal rate: 1.5% a month is 18% a year. To include compounding, use the effective rate formula instead: (1 + 0.015)^12 - 1 = 19.562%. Quoting the 18% as the rate and earning or paying 19.562% is the entire gap between APR and APY.
Calculators in this guide
Frequently asked questions
Is APY or APR better?
Neither is better on its own; they measure different things. Look for a high APY when saving and a low APR when borrowing.
Is a 5% APY the same as 5% interest?
Not always. A 5% APY already includes compounding, so the underlying nominal rate is lower: 4.889% if interest compounds monthly. A 5% nominal rate compounded monthly gives a higher 5.116% APY.
Why do lenders advertise APR and banks advertise APY?
Federal rules require it: Regulation Z requires APR disclosure on credit and Regulation DD requires APY disclosure on deposit accounts. Both make offers easier to compare.
Can APR and APY be the same?
Yes, if interest compounds only once a year and no fees are counted. A 4% rate compounded annually has a 4% APY.
How do I calculate monthly interest from an APR?
Divide the APR by 12 and multiply by the balance. At 18% APR, a $5,000 balance accrues about $75 in a month ($5,000 × 0.18 ÷ 12).
This guide is for education and is not financial, tax or legal advice. Confirm figures with a qualified professional or your lender.
Sources
- Consumer Financial Protection Bureau: What is a credit card interest rate? What does APR mean?
- Consumer Financial Protection Bureau: What is the difference between a loan interest rate and the APR?
- Regulation Z, 12 CFR 1026.22: Determination of annual percentage rate
- Regulation DD, 12 CFR 1030 Appendix A: Annual percentage yield calculation