> ## Documentation Index
> Fetch the complete documentation index at: https://docs.exponent.finance/llms.txt
> Use this file to discover all available pages before exploring further.

# Calculate Historical Fee APY

> Calculate annualized fee APY from historical fee growth data

The `MarketThree.calculateHistoricalFeeApy()` static method calculates the annualized fee APY (Annual Percentage Yield) based on historical fee growth data over a specific time period.

## Usage

```typescript theme={null}
import { MarketThree } from "@exponent-labs/exponent-sdk";

// Calculate fee APY over a 24-hour period
const feeGrowthDeltaSy = currentFeeGrowthSy - historicalFeeGrowthSy;
const feeGrowthDeltaPt = currentFeeGrowthPt - historicalFeeGrowthPt;

const apyData = MarketThree.calculateHistoricalFeeApy({
  feeGrowthDeltaSy,
  feeGrowthDeltaPt,
  avgLiquidity: 1000000n,  // Average liquidity in the range
  hoursElapsed: 24,
});

console.log("SY fee APY:", apyData.feeApySy, "%");
console.log("PT fee APY:", apyData.feeApyPt, "%");
console.log("Total fee APY:", apyData.feeApyTotal, "%");
console.log("Total SY fees earned:", apyData.totalFeesSy);
console.log("Total PT fees earned:", apyData.totalFeesPt);
```

## Parameters

| Parameter          | Type     | Required | Description                                      |
| ------------------ | -------- | -------- | ------------------------------------------------ |
| `feeGrowthDeltaSy` | `bigint` | Yes      | Change in global SY fee growth over the period   |
| `feeGrowthDeltaPt` | `bigint` | Yes      | Change in global PT fee growth over the period   |
| `avgLiquidity`     | `bigint` | Yes      | Average liquidity in the range during the period |
| `hoursElapsed`     | `number` | Yes      | Number of hours in the measurement period        |

## Returns

Returns an object with:

```typescript theme={null}
{
  feeApySy: number;
  feeApyPt: number;
  feeApyTotal: number;
  totalFeesSy: bigint;
  totalFeesPt: bigint;
}
```

| Property      | Type     | Description                                       |
| ------------- | -------- | ------------------------------------------------- |
| `feeApySy`    | `number` | Annualized APY for SY fees as a percentage        |
| `feeApyPt`    | `number` | Annualized APY for PT fees as a percentage        |
| `feeApyTotal` | `number` | Combined annualized APY (SY + PT) as a percentage |
| `totalFeesSy` | `bigint` | Total SY fees earned during the period            |
| `totalFeesPt` | `bigint` | Total PT fees earned during the period            |

## Calculation Details

The APY calculation follows these steps:

1. Calculate total fees earned using Q64.64 math:
   ```
   totalFees = (feeGrowthDelta * avgLiquidity) >> 64
   ```

2. Calculate annualization factor:
   ```
   annualizationFactor = 8760 / hoursElapsed  // 8760 = hours per year
   ```

3. Calculate APY:
   ```
   feeApy = (fees / avgLiquidity) * annualizationFactor * 100
   ```

If `avgLiquidity` is 0 or `hoursElapsed` is 0, all return values will be 0.