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APR vs APY — the DeFi math everyone skips 
Percentages are short, sharp, and dangerously ambiguous. In DeFi they’re everywhere — but two near-identical-looking acronyms, APR and APY, behave very differently. That small difference can mean you earn tens or hundreds of dollars more (or less) over time. Below I’ll explain both clearly, show the formulas, run simple numeric examples, and explain why an open APR/APY calculator matters for on-chain finance.

Definitions 
APR — Annual Percentage Rate
The nominal yearly interest rate.Usually does not include the effect of compounding (interest on interest).Common in contexts where rewards are paid out but not automatically reinvested.
APY — Annual Percentage Yield
The effective yearly return after compounding is taken into account.Shows the real growth of your money if interest is reinvested at the stated frequency.APY ≥ APR (equal only when there’s no compounding).

The math 
If a nominal APR is r (as a decimal) and interest compounds n times per year, the APY is:

\text{APY} = \left(1 + \frac{r}{n}\right)^{n} - 1

If compounding is continuous (mathematically), the formula becomes:

\text{APY}_{\text{continuous}} = e^{r} - 1

To turn APY back into an equivalent nominal APR (for a given n) you can invert the first formula.

Worked examples — do the digit-by-digit math
Start: $1,000 deposit, nominal APR = 10% (r = 0.10).
Simple interest (APR, no compounding) for one year:

\text{FV} = 1000 \times (1 + 0.10) = 1100 \quad\text{(gain = \$100)}

Monthly compounding (n = 12):

\text{APY} = \left(1 + \frac{0.10}{12}\right)^{12} - 1 \approx 0.104713\ \Rightarrow\ \text{FV} \approx 1000 \times 1.104713 = 1104.71

Daily compounding (n = 365):

\text{APY} \approx (1 + \tfrac{0.10}{365})^{365} - 1 \approx 0.105156\ \Rightarrow\ \text{FV} \approx 1105.16

Over multiple years compounding accelerates differences. Example, 5 years, monthly compounding:

\text{FV} = 1000 \times \left(1 + \frac{0.10}{12}\right)^{12\times 5} \approx 1645.31

These small percentage-point differences add up over time.

Why people get confused in DeFi
Platforms mix terminology. One screen shows “10% APR”, another “10.47% APY” — and users don’t always know if rewards are auto-compounded or require manual re-staking.Reward mechanics vary. Rewards might be distributed continuously, hourly, or only at epoch end; token prices change; some systems auto-restake, others don’t.Fees & slippage. Protocol fees, withdrawal fees, and gas costs reduce effective returns — often omitted from headline APR/APY.Non-fixed rewards. Many farming/staking yields depend on network activity, token emissions, or governance decisions — the “projected” number can change dramatically.Impermanent loss (LPs). Liquidity provision has an entirely different risk/return profile — APR/APY alone doesn’t capture token price divergence.

How an APR/APY calculator helps (practical benefits)
Converts headline rates into tangible outcomes. Instead of guessing, you can see final balances for different deposit sizes, times, and compounding frequencies.Makes compounding visible. Compare monthly vs. daily compounding (or continuous) side by side.Promotes realistic expectations. If a yield is volatile or requires manual reinvestment, the calculator lets you model “what-if” scenarios — including lower reinvestment frequency or fees.Education by doing. Users learn that “10% APR” ≠ “10% APY” unless there’s no compounding, helping reduce speculation-based decisions.
(If you want to try one, a practical tool is available at tools.ston.fi/apy-calculator-a... — it lets you plug in deposits, rates, compounding frequency, and timeframes to see modeled outcomes.)

Quick checklist before trusting a yield number
Is the rate APR or APY? If it’s APR, ask how compounding (if any) works.How often does compounding happen? (Daily, hourly, continuously, or manual?)Are fees or performance cuts already factored in? If not, subtract them in your model.Is the reward token volatile? Projected returns in USD depend heavily on token price moves.Is there lockup or withdrawal cost? Factor those into your effective yield.For LPs: model impermanent loss and trading fees vs. reward income.

Final thought — build literacy into product design
As DeFi matures, transparency tools (open calculators, clear labels, simulators) become as important as APYs themselves. A public APR/APY calculator shifts the focus from flashy percentages to the mechanics behind them — and that’s exactly the kind of financial-literacy infrastructure that helps ecosystems grow responsibly.

TL;DR
APR = nominal yearly rate (no compounding).APY = actual yearly yield including compounding.Use the formula to convert APR → APY for n compounding periods.Small differences in compounding frequency compound into meaningful dollar differences over time.Always model fees, token volatility, and reinvestment behavior — and use an APR/APY calculator to make the math concrete.
Try the calculator: tools.ston.fi/apy-calculator-a...
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