APY Calculator
APY (Annual Percentage Yield) is the effective rate you actually earn on a savings product after compounding. A 5% nominal rate compounded daily is worth more than a 5% rate compounded annually. This calculator converts between nominal rate and APY for any compounding frequency, and is the right tool to compare a high-yield savings account to a CD.
How to calculate APY
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1
Enter the nominal rate
The interest rate before compounding. Often labelled "interest rate" on bank disclosures, separate from the APY number.
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2
Pick compounding frequency
Most US savings accounts compound daily. CDs may compound monthly, quarterly or annually. The frequency affects the APY.
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3
See the APY
Output is the effective annual rate. A 5.0% nominal rate compounded daily yields 5.127% APY; monthly yields 5.116%; annual yields 5.000%.
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4
Compare accounts
APY is the fair comparison number across products. Banks are legally required to publish it under Regulation DD.
The APY formula
APY = (1 + r/n)^n - 1
Where:
- r = nominal annual rate (decimal, e.g. 0.05 for 5%)
- n = compounding periods per year
Compounding frequency impact
For a 5.00% nominal rate:
| Compounding | Periods/year | APY | Extra earnings on $10,000 |
|---|---|---|---|
| Annually | 1 | 5.000% | - |
| Semi-annually | 2 | 5.063% | +$6 |
| Quarterly | 4 | 5.095% | +$9 |
| Monthly | 12 | 5.116% | +$12 |
| Daily | 365 | 5.127% | +$13 |
| Continuously | ∞ | 5.127% | +$13 |
After daily compounding, further frequency (hourly, continuous) barely moves the needle, the marginal APY gain is in the fifth decimal.
APY vs. APR
| Metric | Used for | Compounding effect |
|---|---|---|
| APY | Savings, CDs | Included |
| APR | Loans, credit | Not directly |
A 5% savings account has APY > 5% after compounding. A 5% loan has APR = 5% with compounding implicit in the monthly payment schedule. Banks use APY because it looks bigger and is legally the honest number for deposits. Lenders use APR because TILA requires it.
Break-even: CD vs. high-yield savings
A 12-month CD at 5.10% APY vs. a variable high-yield savings account at 4.80% APY:
- CD is better by 0.30% × $10,000 = $30 over the year.
- But if the variable savings rate rises above 5.10% mid-year, the savings account wins.
- CD has an early withdrawal penalty (usually 3-6 months of interest).
Rule of thumb: lock a CD when you believe rates are near the peak. Stay flexible when you think rates are still rising.
Why 5.127% is the limit as n → ∞
Because (1 + r/n)^n approaches e^r as n grows. For r = 0.05, e^0.05 - 1 = 0.05127. That is the continuously-compounded APY, the theoretical ceiling for any compounding frequency.
Frequently Asked Questions
APR is a simple annual rate without compounding, used for loans and disclosed under TILA. APY includes compounding, used for deposits and disclosed under Regulation DD. For the same nominal rate, APY > APR unless compounding is annual, in which case they are equal.
The bank calculates interest daily (365 periods per year, maximising APY) but adds it to your balance once a month. The APY is unchanged, what changes is when interest starts earning interest on itself (monthly).
On a variable-rate high-yield savings account, usually within a few days to a few weeks. On a fixed-rate CD, no, your APY is locked until maturity. That is the tradeoff between the two products.
No. APY is always greater than or equal to the nominal rate. The only time they are equal is when compounding is annual (or effectively annual, some simple-interest products).
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