APY Calculator
Convert between annual percentage yield (APY) and nominal interest rate at any compounding frequency. Use it to compare savings, CD, and money market offers on equal terms.
Convert Rate ↔ APY
The stated rate before compounding (also called the APR on savings accounts).
A 5.00% nominal rate compounded monthly earns the same as a flat 5.1162% rate without compounding.
Free to embed on any site. Paste the iframe below — it loads our hosted APY Calculator with a small attribution link back to CalcSystems.
APY vs. APR vs. Nominal Rate
Three rate terms get used interchangeably in everyday language but mean different things:
- Nominal rate — the stated annual interest rate before any compounding effect. Sometimes called the "stated rate" or, on savings products, the "interest rate." If you see a CD offer at "5.00% interest, compounded monthly," that 5.00% is the nominal rate.
- APY (Annual Percentage Yield) — the effective rate after compounding is applied. Always equal to or greater than the nominal rate; the gap widens as compounding gets more frequent. Banks must advertise deposit accounts in APY under the Truth in Savings Act, so APY is the right number to compare savings, CD, money market, and HYSA offers.
- APR (Annual Percentage Rate) — used for loans and credit cards, not deposits. Represents the annualized cost of borrowing, including certain fees, but by U.S. convention does not include intra-year compounding. APR ≤ APY for the same underlying rate.
For deposit comparisons: only compare APYs. For loan comparisons: only compare APRs. Mixing the two distorts the comparison — a 5.00% APR loan and a 5.00% APY savings account are not the same rate.
APY Conversion Table
The APY for common nominal rates at each compounding frequency. Notice how once compounding is monthly or more frequent, additional compounding adds only a fraction of a basis point.
| Nominal Rate | Daily | Monthly | Quarterly | Semi-annual | Annual | Continuous |
|---|---|---|---|---|---|---|
| 1.00% | 1.0050% | 1.0046% | 1.0038% | 1.0025% | 1.0000% | 1.0050% |
| 2.00% | 2.0201% | 2.0184% | 2.0151% | 2.0100% | 2.0000% | 2.0201% |
| 3.00% | 3.0453% | 3.0416% | 3.0339% | 3.0225% | 3.0000% | 3.0455% |
| 4.00% | 4.0808% | 4.0742% | 4.0604% | 4.0400% | 4.0000% | 4.0811% |
| 5.00% | 5.1267% | 5.1162% | 5.0945% | 5.0625% | 5.0000% | 5.1271% |
| 6.00% | 6.1831% | 6.1678% | 6.1364% | 6.0900% | 6.0000% | 6.1837% |
| 7.00% | 7.2501% | 7.2290% | 7.1859% | 7.1225% | 7.0000% | 7.2508% |
| 8.00% | 8.3278% | 8.3000% | 8.2432% | 8.1600% | 8.0000% | 8.3287% |
| 10.00% | 10.5156% | 10.4713% | 10.3813% | 10.2500% | 10.0000% | 10.5171% |
Each cell shows the APY for the row's nominal rate at the column's compounding frequency. The "Continuous" column is the e^r − 1 limit and represents the theoretical upper bound for a given nominal rate.
Worked Example: 5.00% Rate, Three Compounding Choices
A bank quotes a savings account at "5.00% interest." Three banks compound differently. Plug in the formulas:
- Annual compounding (n = 1): APY = (1 + 0.05/1)^1 − 1 = 5.0000%. The nominal rate equals the APY.
- Monthly compounding (n = 12): APY = (1 + 0.05/12)^12 − 1 = 1.05116 − 1 = 5.1162%. The first month earns 0.05/12 = 0.4167%; that 0.4167% then earns interest itself the next month, and so on.
- Daily compounding (n = 365): APY = (1 + 0.05/365)^365 − 1 = 5.1267%. Only ~1 basis point higher than monthly.
- Continuous compounding: APY = e^(0.05) − 1 = 5.1271%. Just 0.4 basis points above daily — the upper bound.
On a $10,000 deposit held for one year, those four choices return $10,500.00, $10,511.62, $10,512.67, and $10,512.71. The first $1.27 of incremental interest from going annual → daily is real, but the next $0.04 from going daily → continuous is essentially noise. This is why "compounded daily" is a marketing phrase more than a meaningful financial advantage.
How Much Does an APY Earn in a Year?
APY is the effective annual rate, so the simplest way to read it is: a deposit held for one full year at X% APY grows by exactly X% — no compounding adjustment needed. Some quick reference points at typical 2026 high-yield savings and CD rates:
| Deposit | 3.50% APY | 4.00% APY | 4.50% APY | 5.00% APY |
|---|---|---|---|---|
| $1,000 | $35 | $40 | $45 | $50 |
| $5,000 | $175 | $200 | $225 | $250 |
| $10,000 | $350 | $400 | $450 | $500 |
| $25,000 | $875 | $1,000 | $1,125 | $1,250 |
| $50,000 | $1,750 | $2,000 | $2,250 | $2,500 |
| $100,000 | $3,500 | $4,000 | $4,500 | $5,000 |
These are pre-tax, gross interest figures over a full year on a flat balance — the same number you'd see on a year-end 1099-INT before federal and state income tax. For multi-year projections with ongoing contributions, use the compound interest calculator. For a fixed-term deposit, the CD calculator handles the same math with a maturity date and early-withdrawal penalty model.
Frequently Asked Questions
What is APY? +
APY (Annual Percentage Yield) is the effective annual rate of return on a deposit account after accounting for compounding. Unlike a nominal interest rate, APY tells you what you actually earn over a full year — so it's the right number to compare savings, CD, and money market offers across banks. The Truth in Savings Act requires U.S. banks to advertise deposit accounts using APY.
How is APY calculated? +
APY uses the formula APY = (1 + r/n)^n − 1, where r is the nominal annual interest rate (as a decimal) and n is the number of compounding periods per year. For continuous compounding, the formula is APY = e^r − 1. For example, a 5.00% nominal rate compounded monthly gives APY = (1 + 0.05/12)^12 − 1 ≈ 5.1162%, while compounded daily gives ≈ 5.1267%.
What is the difference between APY and APR? +
APY is used for savings and deposit accounts and includes the effect of compounding interest you earn. APR (Annual Percentage Rate) is used for loans and credit cards and represents the annualized cost of borrowing — including some fees but, by U.S. convention, not including the effect of compounding within the year. For a single account at a single rate, APY ≥ APR (they're equal only when compounding is annual). Banks use APY to make savings rates look as high as possible; lenders use APR to make borrowing rates look as low as possible. See the side-by-side breakdown above.
How do I convert nominal rate to APY? +
Pick the compounding frequency, then apply APY = (1 + r/n)^n − 1. For 5% nominal compounded monthly: APY = (1 + 0.05/12)^12 − 1 = 1.05116 − 1 = 0.05116 = 5.116%. The calculator above does this for any frequency, including continuous compounding (e^r − 1) which represents the theoretical upper bound for a given nominal rate.
How do I convert APY to nominal rate? +
Reverse the formula: r = n × ((1 + APY)^(1/n) − 1) for finite compounding, or r = ln(1 + APY) for continuous compounding. For 5% APY compounded monthly: r = 12 × (1.05^(1/12) − 1) = 12 × 0.004074 = 4.889% nominal. The same APY corresponds to a slightly lower nominal rate as compounding gets more frequent.
Why are daily and monthly APYs so close? +
Once compounding is reasonably frequent, additional frequency stops mattering much. At a 5% nominal rate, monthly compounding gives 5.1162% APY and daily compounding gives 5.1267% APY — only a 1-basis-point difference. The continuous-compounding limit is 5.1271%, just 0.4 basis points higher than daily. So a bank advertising "daily compounding" instead of "monthly compounding" is offering a marginal benefit on most savings products.
Does APY include taxes or inflation? +
No. APY is a pre-tax, pre-inflation gross return. To get an after-tax APY, multiply by (1 − marginal tax rate): a 5% APY in the 24% federal bracket is an after-tax 3.80% APY. To get a real (inflation-adjusted) APY, use the Fisher relation: real APY = (1 + APY) ÷ (1 + inflation) − 1. At 5% APY and 3% inflation, real APY ≈ 1.94%.