# Deconstructing the Weighted Percentage (T\_p) Calculation

In ZeroLend's model, T\_p represents the Total or Weighted Percentage, crucial for determining rewards. This metric combines the proportions of dynamic Liquidity Provision (dLP\_p) and single-staked $ZERO (Z\_p) relative to the total USD value of a user's lending deposits. Here's a clearer breakdown:

### **Calculating zLP\_p and Z\_p** 

**zLP\_p Calculation**: Measures the USD value of zLP locked, factoring in the double valuation of $ZERO within LP tokens.

$$
zLP\_p = \frac{zLP}{Deposits}  = \frac{$\textrm{ZERO}\_2 \times 2}{Deposits}
$$

**Note:** $$$\textrm{ZERO}\_2$$ adjusts with LP token ratios, while $veZERO earnings depend solely on the $ZERO quantity at deposit time.

**Z\_p Calculation**: Relates to the USD value of $ZERO locked in single asset staking. 

$$
Z\_p = \frac{$\textrm{ZERO}\_1}{Deposits}
$$

Combining for Total Percentage (T\_p)

$$
T\_p = 4 \times zLP\_p+1\times Z\_p = 4 \times \frac{$\textrm{ZERO}\_2 \times 2}{Deposits} + 1 \times \frac{$\textrm{ZERO}\_1}{Deposits}
$$

and, 

$$
f(T\_p) = f(4 \times \frac{$\textrm{ZERO}\_2 \times 2}{Deposits} + 1 \times \frac{$\textrm{ZERO}\_1}{Deposits}) = \begin{cases}
0 & \text{if } 0.00 \leq T\_p< 0.10 \ 0.5 & \text{if } 0.10 \leq T\_p <0.15\ 0.75 & \text{if } 0.15 \leq T\_p < 0.20 \ 1.0 & \text{if } 0.20 \leq T\_p <0.25\ 1.1 & \text{if } 0.25 \leq T\_p < 0.30 \ 1.25 & \text{if } 0.30 \leq T\_p <0.40\ 1.5 & \text{if } 0.40 \leq T\_p < 0.50 \ 2.0 & \text{if } 0.50 \leq T\_p \\

\end{cases}
$$

This function assigns reward levels based on the calculated T\_p value, with different tiers from 0 to 2.0, enhancing rewards progressively as T\_p increases.

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This functionality is scheduled to go live shortly.&#x20;
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