APY and APR are both yearly percentages, which is why they get mixed up, but they answer different questions. APY tells a saver what a deposit earns once interest compounds. APR tells a borrower the yearly cost of credit, sometimes including fees, without compounding. Federal law decides which one you are shown, so the label on a rate says as much about the product as the number does. This comparison sits in the returns math section of the safe investments hub.
What is the difference between APY and APR?
APY includes compounding and APR does not: APY is a deposit's yearly return with interest reinvested, while APR is a yearly rate before compounding.
On the same underlying rate, the APY is always equal to or higher than the APR, because interest that is credited during the year starts earning interest of its own. The two match only when interest is paid once a year. The bigger differences are legal and practical:
| Feature | APY (annual percentage yield) | APR (annual percentage rate) |
|---|---|---|
| Where you see it | Savings, checking, money market deposit accounts and CDs | Loans, mortgages and credit cards |
| Counts compounding | Yes, over a 365-day year | No |
| Counts fees | No, interest only | Closed-end loans: finance charges such as origination fees and points. Cards: no |
| Federal rule | Truth in Savings Act, Regulation DD (12 CFR 1030) | Truth in Lending Act, Regulation Z (12 CFR 1026) |
| Precision required | Two decimals, accurate within 0.05 point | Within 1/8 point on most loans, 1/4 point on irregular ones |
| Basic math | (1 + rate ÷ n)^n − 1 | Periodic rate × periods a year, or the loan's yield after fees |
| Better for you when | Higher, if you are saving | Lower, if you are borrowing |
One wrinkle trips people up: under Regulation DD, a bank may call a deposit account's plain interest rate an "annual percentage rate" as well. So "APR" on a savings disclosure means the rate before compounding, not a borrowing cost.
How do you calculate APY from an interest rate?
Divide the annual interest rate by the number of compounding periods, add one, raise the result to that number of periods, and subtract one.
APY = (1 + r ÷ n)^n − 1, where r is the annual rate and n is compounding periods a year
Regulation DD's Appendix A states the same idea from the bank's side, using the dollars an account pays over a term. Banks must use it for the APY they advertise:
APY = 100 × ((1 + interest ÷ principal)^(365 ÷ days in term) − 1)
The regulation assumes the principal and interest stay on deposit for the whole term, treats accounts with no maturity as 365-day terms, and leaves bonuses out.
Worked example: A 4.40% savings rate compounded daily
- Daily rate: 4.40% ÷ 365 = 0.012055% a day
- APY: (1 + 0.044 ÷ 365)^365 − 1 = 0.04498, which rounds to 4.50%
- On $10,000 left alone for 365 days: $449.80 of interest, against $440.00 at simple interest
- The same 4.40% compounded monthly: (1 + 0.044 ÷ 12)^12 − 1 = 4.49%
Worked example: A 182-day CD and the Appendix A formula
A $10,000 CD pays 4.40% compounded daily for 182 days and earns $221.81.
- APY = 100 × ((1 + 221.81 ÷ 10,000)^(365 ÷ 182) − 1) = 4.50%, the same as the daily-compounding formula gives
- If the CD paid simple interest instead, it would earn $10,000 × 0.044 × 182 ÷ 365 = $219.40, and its APY would be 4.45%
How much does compounding frequency change APY?
At savings-account rates the effect is small, under a tenth of a point at 4%, but at credit card rates daily compounding adds more than 3 points.
| Compounding | Periods a year | APY at a 4% rate | APY at a 24% rate |
|---|---|---|---|
| Annually | 1 | 4.00% | 24.00% |
| Semiannually | 2 | 4.04% | 25.44% |
| Quarterly | 4 | 4.06% | 26.25% |
| Monthly | 12 | 4.07% | 26.82% |
| Daily | 365 | 4.08% | 27.11% |
| Continuously | no limit | 4.08% | 27.12% |
Three patterns stand out. Most of the gain comes from the first steps, annual to semiannual and semiannual to quarterly. Beyond monthly the gains are tiny: at 4%, daily compounding beats monthly by under 0.01 point, and continuous compounding, the mathematical ceiling of e^r − 1, adds almost nothing more. And the gap grows with the rate itself, roughly with its square, which is why compounding frequency matters far more on a credit card balance than in a savings account.
For a savings decision, that means a higher rate beats more frequent compounding almost every time: 4.45% compounded monthly yields 4.54%, more than 4.40% compounded daily at 4.50%. The compound interest guide shows the same effect in dollars over 30 years.
How do banks have to quote APY?
Under the Truth in Savings Act and Regulation DD, a bank that advertises or discloses a deposit rate must state it as an APY, using that term.
The main requirements, from 12 CFR 1030:
- Account disclosures must give both the "annual percentage yield" and the "interest rate," using those terms, plus how often interest is compounded and credited.
- Advertisements that state a rate of return must state it as an APY. The interest rate may appear too, but no more prominently, and the ad must say that fees could reduce earnings.
- Spoken answers to a customer's rate question must give the APY. The interest rate may be added; no other rate may be quoted.
- Rounding: the APY and interest rate are rounded to the nearest hundredth of a point, and the APY counts as accurate if it is within 0.05 point of the Appendix A result.
- Periodic statements show an "annual percentage yield earned," calculated from the interest actually paid and the average daily balance for that period.
The rule has edges. Credit unions are outside Regulation DD, but the NCUA's Part 707 imposes a parallel version in which the APY reflects dividends. And the official interpretation of Regulation DD says the term "account" does not cover government securities or mutual funds, which is why Treasury bills and money market funds quote other yield measures. A money market fund's 7-day yield is a different calculation, explained in the guide to how money market funds work.
How do lenders have to quote APR?
Regulation Z, which carries out the Truth in Lending Act, requires lenders to disclose the APR before a loan is final.
Regulation Z defines the APR as "a measure of the cost of credit, expressed as a yearly rate." On closed-end loans, such as personal loans, auto loans and mortgages, that cost includes finance charges beyond interest, such as origination fees and points, and the disclosure must label it "the cost of your credit as a yearly rate." The disclosed APR must be accurate within 1/8 of a percentage point on regular loans and 1/4 point on irregular ones.
Credit cards and other open-end credit work differently. Their APR is simply the periodic rate multiplied by the number of periods in a year, so it ignores compounding and fees. A card's APR is closer to a bank's interest rate than to its APY.
The Consumer Financial Protection Bureau points out a few gaps in mortgage APRs: on an adjustable-rate mortgage the APR does not show the maximum rate the loan could reach, and on a home equity line of credit the APR does not include fees. On a Loan Estimate, the interest rate appears on page 1 and the APR in the Comparisons section on page 3.
How do you convert APR to APY and back?
To turn a rate into an APY, use (1 + rate ÷ n)^n − 1; to turn an APY back into a rate, use n × ((1 + APY)^(1 ÷ n) − 1).
Rate = n × ((1 + APY)^(1 ÷ n) − 1)
The reverse direction is useful when you have only an APY and want to model the account by hand or check a statement.
Worked example: From a 4.50% APY back to the interest rate
- Compounded monthly: 12 × (1.045^(1 ÷ 12) − 1) = 4.41%
- Compounded daily: 365 × (1.045^(1 ÷ 365) − 1) = 4.40%
- Compounded quarterly: 4 × (1.045^(1 ÷ 4) − 1) = 4.43%
The more often interest compounds, the lower the stated rate needed to reach the same APY.
Worked example: What a 24% credit card APR really costs
- Daily periodic rate: 24% ÷ 365 = 0.065753%
- One 30-day cycle on a $5,000 balance: $5,000 × (1.00065753^30 − 1) = $99.58, against $98.63 without daily compounding
- Carried for a full year with no payments: 1.00065753^365 − 1 = 27.11% effective
- A card charging 2% a month discloses 12 × 2% = 24% APR, but costs 1.02^12 − 1 = 26.82% a year
On most cards you can avoid purchase interest entirely by paying the full balance by the due date each month.
Why can a loan's APR be higher than its interest rate?
A loan's APR exceeds its interest rate when upfront finance charges, such as an origination fee, are added to the yearly cost of borrowing.
The fee is usually taken out of the money you receive, but you still repay interest on the full loan amount. The APR captures that by finding the rate at which the cash you actually got equals the payments you make.
Worked example: A $10,000 personal loan with a $300 fee
Terms: $10,000 at 9% for 36 months, with a $300 origination fee deducted at closing.
- Monthly payment: $10,000 × 0.0075 ÷ (1 − 1.0075^−36) = $318.00
- Total of payments: $318.00 × 36 = $11,448
- Amount financed: $10,000 − $300 = $9,700
- Finance charge: $11,448 − $9,700 = $1,748, made up of $1,448 of interest and the $300 fee
- APR: the monthly rate at which 36 payments of $318.00 are worth $9,700 is 0.9245%, and 0.9245% × 12 = 11.09%
The interest rate is 9%, but the APR is 11.09%. Even the APR understates the yearly cost on a compounding basis: 1.009245^12 − 1 = 11.68%.
Fees weigh more heavily on short loans. The same 9% loan and $300 fee carry an APR of 14.78% over 12 months and 10.31% over 60 months. Compare APRs between loans of similar size and term, and, as the CFPB puts it, compare APRs to APRs, not APRs to interest rates.
How does a T-bill's investment rate compare with APY?
A Treasury bill's investment rate is a simple annual rate, so it sits slightly below the APY you would earn by rolling the bill all year.
A Treasury bill pays no interest along the way; you buy it below face value and collect the full amount at maturity. Treasury calls the resulting yield the coupon equivalent, bond equivalent or investment yield: the return based on the purchase price and a 365- or 366-day year. It runs higher than the bill's discount rate, which is figured on face value over a 360-day year; the guide to the T-bill discount rate vs investment rate covers how each is calculated. To compare a bill with a savings APY, compound the investment rate i over the bill's term of d days:
APY of a bill ≈ (1 + i × d ÷ 365)^(365 ÷ d) − 1
Worked example: October 30, 2026 bill rates converted to APY
- 4-week bill (28 days), 3.98% investment rate: (1 + 0.0398 × 28 ÷ 365)^(365 ÷ 28) − 1 = 4.05% APY
- 13-week bill (91 days), 4.08%: (1 + 0.0408 × 91 ÷ 365)^(365 ÷ 91) − 1 = 4.14% APY
- 26-week bill (182 days), 4.25%: (1 + 0.0425 × 182 ÷ 365)^(365 ÷ 182) − 1 = 4.30% APY
- $10,000 in the 13-week bill earns about $101.72 per roll, or $413.13 over four rolls if the rate held
The conversion assumes you could reinvest at the same rate, which bills do not promise. Bill interest is also exempt from state and local income tax, so a fair comparison with a bank APY is made after tax; the real returns guide walks through that step. The Treasury bill calculator gives the dollar figures for any bill.
What are the risks of comparing APY and APR?
The main risk is comparing numbers that measure different things, such as a savings APY against a bill's investment rate or one loan's rate against another's APR.
- Mismatched labels. A 4.40% interest rate and a 4.45% APY look close, yet the APY may be the lower deal once both are converted. Put every option on the same basis before ranking.
- Rates that change. A variable-rate account's APY is calculated as if today's rate lasts a year. A promotional APY can drop after a few months, and a bank can cut a savings rate at any time; the high-yield savings guide covers how those accounts set and change rates.
- Fees and balance rules. APY ignores monthly fees, and tiered accounts may pay the advertised APY only on part of a balance.
- What APR leaves out. Card APRs ignore compounding, mortgage APRs on adjustable loans do not show the highest possible rate, and HELOC APRs exclude fees.
- Term mismatch. APR spreads fees over the stated term. Repay early and the true cost of the fee per year is higher than the APR showed.
- Tax and inflation. Neither number is what you keep. A 4.50% APY taxed at 22% leaves 3.51%, below the 3.74% inflation rate for September 2026.
- Insurance. An APY says nothing about safety: check whether a deposit is within $250,000 per depositor, per insured bank, per ownership category, explained in the FDIC insurance guide.
To see how long a given APY takes to double your money, the rule of 72 gives a quick estimate, and the compound interest calculator shows the full path.