# How v3 APR is calculated

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In V3 Liquidity and Farms, with the new non-fungible liquidity and customizable price range ability. Each LP position will have its own LP fee and CAKE farming APR.
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The total APR is combined by the LP fee APR and CAKE reward APR

### LP fee

Theoretically speaking, given a price range and liquidity user about to add, we can estimate the expected future 7 days fee as following 

$$
fee\_{next7d} = fee\_{in} \frac{\Delta{L}}{L\_{in} + \Delta{L}}
$$

* $$fee\_{in}$$ : Fee amount accrued in the user specified price range in last 7 days
* $$L\_{in}$$: Current liquidity in the user specified price range
* $$\Delta{L}$$: Liquidity user want to add to the price range

#### Fee in range

For $$fee\_{in}$$, we use the historical trading volume data, fee tier and historical price data to estimate the price in range

$$fee\_{in} = f\_tV\_{7d}\frac{T\_{in}}{T\_{7d}}$$

* $$f\_t$$: Fee tier
* $$V\_{7d}$$: Total trading volume of last 7 days
* $$T\_{in}$$: Duration, measured in seconds, of prices staying within the price range in the past 7 days
* $$T\_{7d}$$: 7 days measured in seconds

### Cake APR

#### Pool Allocation

The total reward cake per second in MC v3 using upkeep and can be derived by `latestPeriodCakePerSecond` 

`cakePerSecond = lastestPeriodCakePerSecond / 1e12 / 1e18`

In each pool, we can use `poolInfo` to get the `poolWeight` by dividing  `poolInfo.allocPoint / totalAllocPoint`

#### Global Cake APR

Global APR calculated using the total amount of active & staked liquidity with the pool CAKE reward emissions.

`APR (global) = (cakePerSecond * 31536000) / (totalAllocPoint / pool.allocPoint) * 100 * cakeUSD / totalStakedLiquidityUSD`

`totalStakedLiquidityUSD` represents the current pool active staked liquidity in USD, composing by all the position ticks in range staked in MasterChef v3.

#### Position Cake APR

APRs for individual positions may vary depend on their price range settings.

$$
ARP\_p = {\frac{USD\_{r}}{USD\_{p}}} {\frac{L\_{p}}{L\_{lm}}}
$$

* $$USD\_r$$: CAKE reward earn USD per year in pool
* $$USD\_p$$: Total USD value in position
* $$L\_{p}$$: Position liquidity
* $$L\_{lm}$$: Total staking liquidity which tracked by LMPool