APR vs APY: What's the Difference (With the Formula)
APR vs APY: APR is the plain annual rate, APY adds compounding. Both formulas, plus exactly how much the gap is worth at 6%.
Written with AI assistance; every figure is checked against our calculators and primary sources, and reviewed by Ethan Ginsberg before publishing.
The bottom line
A 6% APR compounded daily works out to a 6.18% APY — an extra $18.31 a year on $10,000.
The core of APR vs APY is compounding: APR is the simple annual interest rate before compounding, while APY folds compounding in. At a 6% APR compounded monthly, the APY is 6.17%, so $10,000 earns $616.78 in a year instead of $600.00. Lenders quote APR on debt; banks quote APY on deposits, and federal law sets which goes where.
What's the difference between APR and APY?
APR (annual percentage rate) is the nominal yearly rate. It ignores how often interest is added to the balance. APY (annual percentage yield) is the effective rate after compounding is baked in. The more often interest compounds, the more APY pulls ahead of APR.
If an account never compounded more than once a year, APR and APY would be identical. They split apart only because most accounts compound monthly, daily, or continuously.
The Consumer Financial Protection Bureau (CFPB) puts it simply: APY reflects the total interest you earn over a year, taking compounding into account, while a stated interest rate does not.
What are the APR and APY formulas?
Converting one to the other uses the compounding count n (periods per year):
APY from APR:
APY = (1 + APR / n)^n − 1
APR from APY:
APR = n × [ (1 + APY)^(1/n) − 1 ]
Plug in 6% APR (0.06) compounded monthly (n = 12):
APY = (1 + 0.06 / 12)^12 − 1
= (1.005)^12 − 1
= 0.061678 = 6.1678%
That 6.1678% rounds to the 6.17% APY a bank would advertise.
How big is the gap between APR and APY at 6%?
Here is the same 6% APR on a $10,000 balance held for one year at four compounding frequencies. The APY and the dollar interest climb as compounding gets more frequent.
| Compounding | APR | APY | Interest on $10,000/yr |
|---|---|---|---|
| Annual (n=1) | 6.00% | 6.00% | $600.00 |
| Quarterly (n=4) | 6.00% | 6.14% | $613.64 |
| Monthly (n=12) | 6.00% | 6.17% | $616.78 |
| Daily (n=365) | 6.00% | 6.18% | $618.31 |
Going from annual to daily compounding adds $18.31 over the year on $10,000. Same headline rate, more frequent crediting.
Run your own APR and APY numbers in the compound interest calculator.
When is APR used versus APY?
The two rates live in different parts of the law, which is why you rarely see both on the same product.
| Attribute | APR | APY |
|---|---|---|
| Used on | Loans, credit cards, mortgages | Savings, CDs, money market, checking |
| You are | Paying interest | Earning interest |
| Governing rule | Truth in Lending Act (Reg Z) | Truth in Savings Act (Reg DD) |
| Includes compounding? | No | Yes |
| Includes fees? | Loan APR can include certain fees | No |
One wrinkle: loan APR can bundle in some up-front costs such as origination fees and points, so a mortgage APR is usually a bit higher than the note rate. Deposit APY is purely about interest and compounding, with no fees mixed in.
Why does the law require each one?
Congress created two disclosure regimes:
- The Truth in Lending Act, implemented through Regulation Z, forces lenders to disclose an APR so borrowers can compare debt costs on a common basis.
- The Truth in Savings Act, implemented through Regulation DD, requires depository institutions to disclose APY so savers can compare returns on a common basis.
Because APY already standardizes for compounding, two CDs advertising 5.00% APY pay the same regardless of whether one compounds daily and the other monthly. That is the point of the metric: it strips out the compounding-frequency noise so the headline number is directly comparable.
The takeaway is mechanical, not advisory. On money owed, a higher APR costs more. On money saved, a higher APY earns more. The conversion between them is the same compounding formula running in opposite directions.
This is educational only and not financial advice. The rates and dollar figures above are illustrative; the formulas are exact, but your actual APR, APY, and compounding frequency will be set by your specific lender or bank. We share the math and the public sources so you can verify it yourself.
Sources
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