# Precise APY calculations

## General (**Commonly used formulas)**

#### User’s reward allocation for a singular position <a href="#users-reward-allocation-for-a-singular-position" id="users-reward-allocation-for-a-singular-position"></a>

$$
R\_{D%} = \frac{C\_x}{\sum\_{n=1}^{users}C\_n}
\\\
\C\_x = T \cdot M
$$

$$\\\textbf{Where:}\R\_{D%} ; -; allocation ; of ; rewards ; for ; the ; user ; X's ; position\C\_x, C\_n  -  ; contribution ; of ; the ; user ; X,; N \users ;  -  ; amount ; of ; positions ; in ; the ; Policy ; Book\T ;  -  ; user ; X's ; staked ; funds ; of ; the ; position\M ;  -  ; user ; X's ; multiplier ; of ; the ; position$$

#### User’s yearly rewards for position X <a href="#users-rewards-for-the-position" id="users-rewards-for-the-position"></a>

$$
R\_x= RPB \cdot BPY \cdot R\_{D%}
$$

$$\\\textbf{Where:}\R\_x  -  ; yearly; rewards ; for ; the ; user ; X's ; position\RPB ;  -  ; Policy ;Book's ; reward ; per ; block\BPY ;  -  ; blocks ; in ; a ; year\R\_{D%} ;  -  ; allocation ; of ; rewards ; for ; the ; user ; X's ; position$$

**Policy Book X reward multiplier calculation**

**Where:**\
**UR -** Utilization Ratio\
**RM -** Reward Multiplier

{% hint style="info" %}
***These constants have been skipped in the formulas for clarity's sake.***\
Base RM = 1\
Min. RM = 0.15\
Max. RM = 2\
Risky UR = 85%\
Moderate UR = 50%
{% endhint %}

$$
UR <  50% \implies RM\_x=\frac{UR-1%}{50%}\*(1-0.15)+0.15
$$

$$
50 %< UR < 85% \implies RM\_x=1
$$

$$
UR >  85% \implies RM\_x= 1+\frac{(2-1)\*(UR-85%)}{100%-85%}
$$

**Policy Book X reward allocation calculation**

$$
R\_{P%} = \frac{RM\_x \cdot CPIP\_x}{\sum\_{n=1}^{pools}(RM\_n \cdot \ CPIP\_n)}
$$

$$\\\textbf{Where:}\R\_{P%} ;  -  ; allocation ; of ; rewards ; for ; the ; Policy ; Book; X\RM\_x ;  -  ; Reward ; Multplier ; of ; the ; Policy ; Book ; X\CPIP\_x ;  -  ; staked ; DEINxCover ; in ; Policy ; Book ; X\pools ;  -  ; number ; of ; whitelisted ;pools$$

## Underwriting Position APY

$$
APY\_x = \frac{R\_x\cdot DEIN\_{price}}{T\_x}
$$

$$\\\textbf{Where:} \R\_x ;  -  ; yearly ;rewards ; for ; the ; position ; x\T\_x ;  -  ; staked ; funds ; in ; the ; position ; x\DEIN\_{price} ;  -  ; price ; of ; DEIN$$

## Underwriting Max (General) APY <a href="#max-general-apy" id="max-general-apy"></a>

This is the APY used on general Policy Book views. It's an estimation of the biggest possible return, it assumes the minimal investment and longest staking duration.

$$
\APY\_{max} = \frac{R\_x \cdot DEIN\_{price}}{T\_x}
$$

$$\\\textbf{Where:}\R\_x ; is ; calculated ; for ; C\_x = 500 \T\_x = 100 \DEIN\_{price} - ; price ; of ; DEIN$$

<br>