APY Calculator
An APY calculator turns an interest rate into the annual percentage yield with APY = (1 + r ÷ n)n − 1, where r is the yearly rate and n is the number of compounding periods. For example, 4% compounded daily gives (1 + 0.04 ÷ 365)365 − 1 ≈ 4.0808%, so $10,000 earns about $408.08 in one year.
Show steps
- Write the rate as a decimal: r = 4% ÷ 100 = 0.04.
- Daily compounding: the daily rate is r ÷ 365 = 0.04 ÷ 365 ≈ 0.000109589.
- Interest is added 365 times in a year, so $1 grows to (1 + 0.000109589)^365 ≈ 1.04080849. Each period earns interest on the interest already added.
- Subtract the starting $1: APY = 1.04080849 − 1 = 0.04080849 = 4.0808%. Regulation DD rounds the disclosed APY to the nearest 0.01%, so it appears as 4.08%.
- Compounding adds 0.0808 percentage points to the 4% rate. With annual compounding the APY would equal the rate, 4%.
- Interest on $10,000.00 for one year: $10,000.00 × 0.04080849 ≈ $408.08, for a balance of $10,408.08.
APY by compounding frequency
| Compounding | APY | 1-year interest |
|---|---|---|
| Annually | 4% | $400.00 |
| Semiannually | 4.04% | $404.00 |
| Quarterly | 4.0604% | $406.04 |
| Monthly | 4.0742% | $407.42 |
| Daily (÷ 365) | 4.0808% | $408.08 |
| Daily (÷ 360, 365 days) | 4.1387% | $413.87 |
| Continuously | 4.0811% | $408.11 |
How to use the APY calculator
- APY from rate: enter the interest rate and how often it compounds to get the APY and one year of interest on a deposit.
- Rate from APY: enter the APY a bank advertises to find the interest rate behind it for any compounding.
- Interest earned: enter a deposit, an APY or rate, a term and an optional monthly deposit to see the balance and the interest.
- Compare two: enter two accounts, each quoted as an APY or a nominal rate, to see which earns more and by how much.
- APY from interest: enter the interest you earned, the principal and the days, and the calculator applies the Regulation DD formula.
APY formula
Regulation DD defines the annual percentage yield as a rate reflecting the total interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period. The interest rate itself is the annual rate that does not reflect compounding. The formula links them:
APY = (1 + r ÷ n)n − 1
- r is the yearly interest rate as a decimal (4% = 0.04).
- n is the number of times interest compounds in a year: 365 daily, 12 monthly, 4 quarterly, 2 semiannually, 1 annually.
- For continuous compounding, APY = er − 1.
Worked example. A savings account pays 5% compounded monthly. Each month earns 0.05 ÷ 12 ≈ 0.0041667, and over 12 months $1 grows to (1.0041667)12 ≈ 1.0511619. Subtract 1: the APY is about 5.1162%, which a bank would disclose as 5.12%.
How to find the interest rate from an APY
Undo the formula by taking the n-th root:
r = n × ((1 + APY)1/n − 1)
An account advertising 4.50% APY with daily compounding pays a rate of 365 × (1.0451/365 − 1) ≈ 4.4020%. If it compounds once a year, the rate and the APY are the same.
Regulation DD APY formula and the Appendix A example
Banks in the United States disclose APY under the CFPB’s Regulation DD (Truth in Savings). Appendix A gives the general formula, which works from the interest actually paid:
APY = 100 × [(1 + Interest ÷ Principal)365 ÷ Days in term − 1]
Worked example from Appendix A. A six-month CD of $1,000 pays $30.37 of interest over 182 days. Interest ÷ principal = 0.03037, and 365 ÷ 182 ≈ 2.005495. Then (1.03037)2.005495 − 1 ≈ 0.061837, so the APY is 6.18%. The APY from interest tab is pre-filled with this example.
The rule also says the disclosed APY is rounded to the nearest one-hundredth of a percentage point (0.01%), and counts as accurate if it is within 0.05 percentage point of the exact figure.
Daily compounding explained
Regulation DD requires banks to calculate interest on the full principal in an account each day, using the daily balance or average daily balance method, with a daily rate of at least 1/365 of the interest rate (1/366 is allowed in a leap year). At 4%, the daily rate is 0.04 ÷ 365 ≈ 0.000109589. Applied 365 times, $1 grows to about 1.0408085, an APY of 4.0808%.
The official interpretation also lets a bank use a larger daily rate, such as 1/360 of the interest rate, as long as it applies it 365 days a year. That raises the yield: 4% becomes (1 + 0.04 ÷ 360)365 − 1 ≈ 4.1387%. Choose Rate ÷ 360, 365 days under Daily rate to see the difference.
More frequent compounding always adds a little, but the gain shrinks: at 4%, monthly gives 4.0742%, daily 4.0808% and continuous 4.0811%.
APY quick-reference table
| Interest rate | APY, monthly | APY, daily | 1 year on $10,000 (daily) |
|---|---|---|---|
| 1% | 1.0046% | 1.0050% | $100.50 |
| 2% | 2.0184% | 2.0201% | $202.01 |
| 3% | 3.0416% | 3.0453% | $304.53 |
| 4% | 4.0742% | 4.0808% | $408.08 |
| 5% | 5.1162% | 5.1267% | $512.67 |
| 6% | 6.1678% | 6.1831% | $618.31 |
Interest earned with APY over time
Because the APY already includes compounding, a deposit P grows to P × (1 + APY)t after t years. $10,000 at 4% APY for 5 years becomes 10,000 × 1.045 ≈ $12,166.53, so the interest is $2,166.53.
Monthly deposits grow by the monthly equivalent of the APY, g = (1 + APY)1/12. Adding $100 at the end of each month to the same account for 5 years gives a balance of $18,784.43: $16,000 deposited and $2,784.43 of interest.
How to compare two savings accounts
Turn both quotes into APYs first, because APY puts every compounding schedule on the same footing. Account A pays 4% compounded daily (4.0808% APY). Account B pays 4.05% compounded once a year (4.05% APY). Over 5 years, $10,000 earns $2,213.89 in A and $2,195.80 in B, so A comes out $18.09 ahead even though its quoted rate is lower.
APY vs interest rate vs APR
The interest rate is the yearly rate before compounding; the APY adds the effect of compounding, so it is equal to or higher than the rate. APR is a different measure: the CFPB explains that for credit cards, the yearly interest rate is called the annual percentage rate. When you compare savings accounts, money market accounts or CDs, compare APYs.
Common APY mistakes
- Applying the compounding formula to a number that is already an APY. An APY needs no further compounding for one year.
- Comparing one bank’s interest rate with another bank’s APY.
- Forgetting that savings rates can change; an APY describes a year at today’s rate.
- Expecting the APY to include fees. Fees reduce what you actually earn.
- Dividing a monthly interest figure by the deposit and calling it the APY. Annualize it with the Regulation DD formula instead.
Results are estimates for learning and planning, not financial advice.
Sources
Checked November 2026.
- CFPB, Regulation DD § 1030.2 Definitions (annual percentage yield, interest rate)
- CFPB, Regulation DD Appendix A, Annual Percentage Yield Calculation
- CFPB, Regulation DD § 1030.3 General disclosure requirements (rounding and accuracy)
- CFPB, Regulation DD § 1030.7 Payment of interest (daily rate, 365-day basis)
- CFPB, What is a credit card interest rate? What does APR mean?
APY practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
APY = (1 + 0.06 ÷ 12)^12 − 1 = 1.005^12 − 1 ≈ 0.0617, or 6.17%. 6.00% ignores compounding; 72% multiplies the rate by 12.
With annual compounding there is one period, so the rate equals the APY: r = 1 × (1.05^1 − 1) = 5.00%.
r = 12 × (1.05^(1/12) − 1) ≈ 12 × 0.0040741 ≈ 4.89%. 5.12% is the APY of a 5% rate, the reverse direction.
The APY already includes compounding, so interest = 5,000 × 0.045 = $225.00. Compounding the APY again gives the wrong $230.12.
APY = (1 + 25 ÷ 1,000)^(365 ÷ 182) − 1 = 1.025^2.005495 − 1 ≈ 5.08%. Doubling 2.5% to 5.01% skips the compounding.
Compare APYs. 4% daily is (1 + 0.04 ÷ 365)^365 − 1 ≈ 4.0808%, while 4.10% compounded annually is a 4.10% APY. The higher APY always earns more, whatever the deposit.
Balance = 10,000 × 1.04^3 = $11,248.64. $11,200 is simple interest; $11,274.89 treats 4% as a daily-compounded rate instead of an APY.
APY = (1 + 0.04 ÷ 360)^365 − 1 ≈ 4.1387%, or 4.14%. Using 1/365 instead gives 4.08%.
The disclosed APY is rounded to the nearest one-hundredth of one percentage point, so 5.644% becomes 5.64%. Regulation DD's own commentary uses this example.
Quiz complete
Frequently asked questions
How do you calculate APY?
Divide the yearly rate by the number of compounding periods, add 1, raise to the number of periods, then subtract 1: APY = (1 + r ÷ n)n − 1. For 5% compounded monthly that is about 5.1162%.
Is APY calculated monthly or yearly?
APY is always a yearly figure. Interest may be compounded and credited daily or monthly, but the APY shows what that compounding adds up to over 365 days.
How much interest will $10,000 earn at 4% APY?
About $400 in the first year, because the APY already includes compounding: 10,000 × 0.04 = $400. Over 5 years it earns $2,166.53 if you leave the interest in the account.
What is the difference between APY and interest rate?
The interest rate does not include compounding; the APY does. With annual compounding they are equal. With daily compounding, a 4% rate is a 4.0808% APY.
Does daily compounding make a big difference?
Only a little. At 4%, daily compounding gives 4.0808% against 4.0742% monthly, about $0.66 more a year on $10,000. The rate itself matters far more.
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