APY Calculator
At a fixed 5% APR compounded monthly, a $10,000 deposit has a modeled 5.12% APY and reaches $10,511.62 after one year. This APY calculator converts a nominal annual rate and positive integer compounding frequency into effective annual yield, ending balance, and interest. The model assumes the full deposit remains for one year, the APR and compounding schedule do not change, and no fees, withdrawals, taxes, or tiered balances apply. Compare the result with the institution's official APY and account disclosure before choosing a financial product.
Quick answer
APR is the nominal yearly rate before compounding, while APY is the real yearly yield after compounding is applied.
This estimate assumes one full year at a fixed APR with no extra deposits, withdrawals, fees, or taxes.
What this tells you
- •APR is the nominal yearly rate before compounding, while APY is the real yearly yield after compounding is applied.
- •More frequent compounding usually pushes APY a little above APR, even when the stated rate stays the same.
- •Your deposit amount changes the dollar interest you earn, but it does not change the APY itself.
- •The APR field expects 5 for 5%, not 0.05.
- •Compounds per year must be a positive whole number.
- •The periodic rate equals APR divided by the number of annual compounding periods.
- •A 0% APR returns 0% APY and no modeled interest.
- •The calculator models one opening deposit with no additional transactions.
- •Advertised APY may reflect product-specific balance methods, fees, and eligibility conditions.
How to Use
- 1Enter a positive opening deposit for the one-year dollar illustration.
- 2Enter nominal APR as a percent, such as 5 for 5%. Do not enter an already compounded APY.
- 3Choose the annual compounding frequency stated by the account or scenario.
- 4Calculate and review APY separately from the ending balance and interest dollars.
- 5Check the periodic rate to confirm APR was divided across the expected number of periods.
- 6Repeat with another frequency only when comparing the same nominal APR under alternative schedules.
- 7Read the institution's disclosure for fees, minimum balances, rate tiers, posting rules, and variable-rate terms.
How It Works
Formula
APY = (1 + APR ÷ n)^n - 1
Ending balance = Deposit × (1 + APR ÷ n)^n
Interest earned = Ending balance - Deposit
Example: (1 + 0.05 ÷ 12)^12 - 1 = 0.051162, or 5.12% APYConvert APR to a decimal and divide by n, the positive whole number of annual compounding periods. Add 1, raise the result to n, then subtract 1 for APY. At 5% monthly, the periodic rate is 0.05/12 = 0.0041667. The growth factor is (1.0041667)^12 = 1.0511619, producing about 5.12% APY. Multiplying $10,000 by the full factor gives $10,511.62, and subtracting the deposit gives $511.62.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
A 5% APR savings account compounded monthly
The periodic rate is 5% / 12 = 0.4167% after display rounding. Applying it 12 times produces 5.12% APY, $10,511.62 ending balance, and $511.62 interest.
A 4% APR CD compounded quarterly
Quarterly compounding uses a 1% rate each quarter. Four rounds of compounding lift the one-year yield to 4.06%, so the deposit earns $609.06 over the term shown here.
3.5% APR compounded daily
The model divides 3.5% by 365, giving a displayed periodic rate of 0.0096%. The one-year growth factor produces 3.56% APY and $178.09 interest.
Zero-rate account
A zero periodic rate creates a growth factor of 1. The balance stays $25,000 and interest remains $0 regardless of the selected frequency.
4.8% APR compounded annually
With one annual period, APY equals APR. Multiplying $8,000 by 1.048 gives $8,384, for $384 of modeled interest.
How 5% APR Changes With Compounding Frequency
The same nominal APR produces slightly different APYs depending on how often interest is credited during the year.
| Compounding | Periods per year | APY on 5% APR |
|---|---|---|
| Annual | 1 | 5.00% |
| Semiannual | 2 | 5.06% |
| Quarterly | 4 | 5.09% |
| Monthly | 12 | 5.12% |
| Weekly | 52 | 5.12% |
| Daily | 365 | 5.13% |
APY rises as compounding gets more frequent, but the difference gets small once you move from monthly to weekly or daily compounding.
APY helps compare rates, not every account term
APY puts compounding schedules onto a one-year percentage basis, which helps compare rates. It does not show how fees, withdrawal limits, minimum balances, promotional periods, or changing rates affect a particular customer.
The deposit field is used only for the dollar illustration. APY comes from APR and frequency, so changing deposit size changes ending balance and interest dollars but not the modeled percentage.
Use an advertised APY directly when the institution already provides it. Entering APY as APR and applying compounding again would count the compounding effect twice.
Common mistakes
- Entering APY into the APR field, which counts compounding twice
- Assuming a bigger deposit changes the APY, when it only changes the dollar interest earned
- Comparing accounts with different fees or balance rules as if APY were the whole story
- Typing 0.05 when the field expects 5 for a 5% APR
- Using an advertised APY as the APR input and compounding it again
- Assuming the opening deposit stays eligible for one rate when the account uses balance tiers
- Treating a variable or promotional rate as fixed for the full year
Limitations
This calculator assumes a positive opening deposit, a fixed nonnegative nominal APR for one year, and a positive integer compounding frequency. It models equal periodic compounding with no deposits, withdrawals, fees, taxes, penalties, minimum-balance changes, rate tiers, promotional expiration, or day-count adjustments. Daily compounding uses 365 equal periods. It does not model continuous compounding, leap-year day counts, average daily balance methods, or institution-specific posting rules. Rounded outputs can differ slightly from statements and disclosures.
Embed this calculator on your site
Drop this single line where you want the calculator to appear. It is responsive, mobile-friendly, resizes automatically, and is free to use with attribution.
<script src="https://calctide.com/embed.js" data-tool="apy-calculator" async></script>Preview the embed at /embed/apy-calculator/.