> For the complete documentation index, see [llms.txt](https://openport.gitbook.io/homepage/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://openport.gitbook.io/homepage/welcome-to-the-port/janus-gate/mint-and-redeem.md).

# Mint and Redeem

## 1. Initial Parameter 

For the stable operation and long-term development of PUST assets, in the initial version, the minting limit of PUST will be set. The minting limit of each minting pool: equivalent to 100 million US dollars, of which the minimum dynamic mortgage rate of stablecoin assets is 80%. For rule updates in subsequent versions, please pay attention to the platform's official website or announcement.

## 2. Mint

All minted PUST share the collateral regardless of the collateral rate when the PUST is minted. When minting occurs, the mathematical relationship between collateral and PUST is as follows:

$$P= \overbrace{(Y*P\_y)}^{\text{Value of Collateral}} + \overbrace{(Z*P\_z)}^{\text{Value of PEACE}}$$ 

$$(1-C\_r)(Y*P\_y) = C\_r(Z*P\_z)$$ 

$$P$$ is the units of newly minted PUST

$$C\_r$$ is the collateral ratio

$$Y$$ is the units of collateral

$$P\_y$$ is the price of $$Y$$ in USD

$$Z$$ is the units of PEACE burned 

$$P\_z$$ is the price of PEACE in USD

## 3. Mint Example

Case 1: When the price of USDT is $1, and 200 USDT is used to mint PUST at 100% mortgage rate, the calculation process of the relevant value is as follows.

#### 1. The amount of PEACE needed in collateral

$$(1−1.00)(200∗1.00)=1.00(Z∗Pz) 👇$$ 

$$0=(Z∗Pz)👇$$ 

$$Z=0$$ 

When the collateral ratio is 100% (fully collateralized), minting PUST does not require PEACE.

#### 2. The amount of newly minted PUST

$$P=(200∗1.00)+(0)👇$$ 

$$P=200$$ 

When the collateral ratio is 100%, 200 PUST can be minted out.

\
**Case 2: When the price of USDT is $1, the PEACE is $2, and 120 USDT is used to mint PUST at an 80% mortgage rate, the calculation process of the relevant value is as follows.**

#### 1. The amount of PEACE needed in collateral

 $$(1 - 0.8)(120 \* 1.00) = 0.8(Z\*2.00)👇$$ 

$$Z = 15$$ 

Minting PUST needs to provide 120 USDT and 15 PEACE.

#### 2. The amount of PUST minted out

$$P= (120*1.00) + (15*2.00)$$ 👇

$$P= 150$$ 

When the collateral ratio is 80%, 150 PUST can be minted out.<br>

**Case 3: When the price of USDT is $0.9995, the PEACE is $3.5, and 220 USDT is used to mint PUST at a mortgage rate of 50%, the calculation process of the relevant value is as follows.**

#### 1. The amount of PEACE needed in collateral

$$(1-0.50)(220*0.9995) = 0.50(Z*3.50)$$ 👇

$$Z = 62.8257143$$&#x20;

&#x20;Minting PUST needs to provide 120 USDT and 62.8257143 PEACE.

#### 4. The amount of PUST minted out

$$G = (220*0.9995) + (62.8257143*3.50)$$ 👇

$$G = 439.78$$&#x20;

When the collateral ratio is 50%, 439.78 PUST can be minted out.

## 4. Redeem

When you redeem, When minting occurs, the mathematical relationship between collateral and pUST is as follows\
\
&#x20;$$Y = \dfrac{G\*(C\_r)}{P\_y}$$&#x20;

$$Z = \dfrac{G\*(1-C\_r)}{P\_z}$$&#x20;

$$G$$ indicates the units of PUST redeemed

$$G\_r$$ is the collateral ratio

$$Y$$ is the units of collateral the user obtained

$$P\_y$$ is the price of the collateral in USD

$$Z$$ is the units of PEACE the user obtained

$$P\_z$$ is the price of PEACE in USD

## 5. Redemption Example

Redeem 170 PUST at 65% mortgage rate. USDT’s oracle price is $1, PEACE’s oracle price is $3.75

$$Y = \dfrac{170\*(.65)}{1.00}$$ 👇

$$Z = \dfrac{170\*(.35)}{3.75}$$ 👇

$$Y$$ = 110.5 and $$Z$$ = 15.867

You can get 110.5 USDT from the collateral pool and the newly generated 15.867 PEACE, with an overall value of $170 equal to 170 PUST.

{% hint style="info" %}
Note: In order to simplify the logic and facilitate the demonstration, the calculation of the minting fee (0.5%) and the redemption fee (0.5%) is not included in the above case.
{% endhint %}