APR to APY converter: how much does compounding really add?
Two accounts can quote the same rate and still pay different amounts. Enter a rate and a compounding frequency to see the real yearly yield.
Education only, not investment, tax or legal advice. Crypto-assets are high-risk — risk disclosure.
The short answer
APR is a simple annual rate that ignores compounding. APY is the effective yearly rate once interest starts earning interest. Convert with APY = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods per year. More frequent compounding means a higher APY.
Key takeaways
- APY folds compounding into one number; a nominal rate or APR does not.
- US deposit adverts that state a rate of return must express it as APY under Regulation DD, the Truth in Savings rule.
- The gap between APR and APY grows as the rate rises and as compounding gets more frequent.
- Compare savings by APY, and loans by APR plus the total amount repaid.
How do you use the APR to APY converter?
Three inputs, one answer
- 1
Enter the nominal rate
Type the quoted annual rate before compounding: the interest rate on a savings account, or the APR on a loan or card.
- 2
Pick the compounding frequency
Choose how often interest is added to the balance, from once a year to daily. The account terms say which applies.
- 3
Read the APY and the gap
The result shows the effective annual yield and how many percentage points compounding adds.
The converter assumes the money stays put for a full year with every interest payment left to compound, the same assumption US banks must use when they calculate APY2. Deposit adverts that state a rate of return must express it as APY; the plain interest rate may appear only alongside it, never more prominently6.
What is the difference between APR and APY?
US Truth in Savings rules define an account's interest rate as the annual rate that does not reflect compounding, and the annual percentage yield as a rate reflecting the total interest paid over a 365-day period, based on both the rate and how often it compounds1.
On the borrowing side, the term APR has its own legal meaning. For a credit card or other revolving credit, Regulation Z says the APR is found by multiplying the periodic rate by the number of periods in a year4. A card charging 2% a month is quoted at 24% APR, even though a balance left to grow for a year costs more. A mortgage APR also bundles in points, broker fees and other charges, so it is usually higher than the interest rate5.
Figure · Two rates, two jobs
APR / nominal rate
- Ignores compounding
- Card APR: periodic rate × periods
- Loan APR can include fees
- Used to quote credit costs
APY
- Includes compounding
- Assumes a full 365 days
- Excludes bonuses
- Used to quote savings yields
What is the APY formula?
The converter uses APY = (1 + r ÷ n)^n − 1. Here r is the nominal annual rate as a decimal (4.5% becomes 0.045) and n is the number of compounding periods in a year (12 for monthly, 365 for daily). Multiply by 100 for a percentage.
Regulation DD expresses it in dollars: APY = 100 × [(1 + interest ÷ principal)^(365 ÷ days in term) − 1]2. Its own example: $61.68 of interest over a 365-day year on $1,000 is an APY of 6.17%2. Our converter reproduces that figure: a 6% nominal rate compounded monthly gives 6.1678%, which rounds to 6.17%.
Banks must round the disclosed APY to the nearest hundredth of a percentage point, shown with two decimals3. The converter shows four decimals.
APY for common nominal rates and compounding frequencies (calculated with the converter, rounded to two decimals)
| Nominal rate | Annually | Monthly | Daily |
|---|---|---|---|
| 3% | 3.00% | 3.04% | 3.05% |
| 5% | 5.00% | 5.12% | 5.13% |
| 12% | 12.00% | 12.68% | 12.75% |
| 24% | 24.00% | 26.82% | 27.11% |
Worked example: what does 4.50% compounded daily really pay?
Worked example
A 4.50% savings rate, compounded daily (illustrative)
Enter 4.5 as the rate and 365 as the compounding frequency. The converter returns an APY of 4.6025%, which is 0.1025 percentage points above the nominal rate. A bank would disclose it as 4.60% APY.
On an illustrative $10,000 left untouched for a year, that is about $460.25 of interest, compared with $450.00 if interest were paid only once at year end. Switch the same rate to monthly compounding and the APY falls slightly, to 4.5940%.
At credit-card rates the gap is larger: a 24% APR compounded monthly corresponds to an effective annual rate of 26.82%, if nothing is repaid.
To go the other way, use r = n × [(1 + APY)^(1 ÷ n) − 1]. A 5.00% APY compounded daily implies a nominal rate of about 4.8793%; feeding that back into the converter returns 5.0000%.
What does the converter leave out?
- Rate changes. A variable rate can move; the APY assumes today's rate holds all year.
- Withdrawals and deposits. APY assumes no other transactions during the term2.
- Fees and bonuses. A monthly fee can cancel out the compounding gain; APY counts interest only, not bonuses2.
- Tax and inflation. Interest may be taxed, and rising prices erode it; see the inflation calculator.
- Crypto yields. A crypto platform's "APY" is not a bank deposit rate and may not follow Truth in Savings rules.
Risk warning
A high APY is not a safety rating
A yield shows how interest is calculated, not whether your money is protected. Unusually high yields, especially on crypto platforms, can carry the risk of losing the deposit itself. See our risk disclosure.
Common beginner mistakes
Comparing an APR with an APY
A 5% APR compounded daily and a 5% APY are not the same deal. Convert one into the other before comparing.
Assuming daily compounding doubles returns
At savings-account rates, daily instead of monthly compounding adds only hundredths of a point.
Frequently asked questions
Is APY always higher than APR?
For a positive rate, APY equals the nominal rate with annual compounding and is higher whenever interest compounds more often.
Why does my bank show two different percentages?
The smaller one is usually the interest rate and the larger one the APY. US rules let banks show the interest rate only next to the APY and no more prominently6.
Can I use this for a crypto staking or lending yield?
You can do the arithmetic, but the advertised figure may be calculated differently, change daily or be paid in a token whose price moves.
The bottom line
APY answers "what will I actually earn in a year?"; a nominal rate or APR leaves compounding out. Use the converter to put offers on the same footing, and remember that fees, rate changes, tax and inflation all sit outside the formula.
Sources
- 12 CFR 1030.2 — Definitions (Regulation DD, Truth in Savings) — Electronic Code of Federal Regulations (eCFR), 2026 Primary source
- Appendix A to Part 1030 — Annual Percentage Yield Calculation — Electronic Code of Federal Regulations (eCFR), 2026 Primary source
- 12 CFR 1030.3 — General disclosure requirements (rounding and accuracy rules) — Electronic Code of Federal Regulations (eCFR), 2026 Primary source
- 12 CFR 1026.14 — Determination of annual percentage rate (Regulation Z) — Electronic Code of Federal Regulations (eCFR), 2026 Primary source
- What is the difference between a mortgage interest rate and an APR? — Consumer Financial Protection Bureau Primary source
- 12 CFR 1030.8 — Advertising (permissible rates) — Electronic Code of Federal Regulations (eCFR), 2026 Primary source
How we checked this page: every figure above links to the numbered source it came from. Spotted an error? Tell the desk — see our editorial policy.
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