# Lending

Users can become lenders by depositing their preferred asset that is accepted by the protocol. Deposits can be withdrawn anytime unless every token in a market is borrowed.

Lending interest is distributed through the value appreciation of **oToken**, which is minted to lenders as a deposit receipt.

## oToken

oToken balances represent a depositor's share in the market. The exchange rate with their underlying token, the **oToken** **exchange rate**, increases as deposits accrues interest, appreciating the value of oToken. With time, holders can redeem oToken with a greater number of underlying tokens, enabling depositors to collect interest simply by holding them.

The oToken exchange rate at time $$t$$ is defined as:

$$
oTokenExchangeRate(t) = \frac{totalDeposited(t)+ totalBorrowed(t) - reserves(t)}{oToken Supply(t)}
$$

Where $$totalDeposited(t)$$ and $$totalBorrowed(t)$$ is the amount of money sent into the system and amount of money borrowed by the borrower at time $$t$$. A share of the protocol’s interests is allocated to a collector contract from the ecosystem treasury, saved to the parameter $$reserves(t)$$.  

As the market’s total borrowing balance increases (as a function of borrower interest accruing), the exchange rate between oToken and the underlying asset increases.

The amount of oToken a user receives when depositing underlying asset is calculated using the $$oTokenExchangeRate$$ value using the formula below:

$$
oTokenMinted =\frac{depositAmount}{oTokenExchangeRate(t)}
$$

And amount of underlying asset user receives when oToken is calculated as below:

$$
receiveAmount = oTokenBurned \times oTokenExchangeRate(t)
$$

### Lending Interest Rate

The equation above simply means that all income received through lending, after a small portion is subtracted to deposit into the system's reserve, will be split equally among lenders.

The lending interest rate $$L(t)$$ at time $$t$$ can be re-expressed by the following formula:

$$
L(t) = B(t) \times U(t) \times (1-r)
$$

Where $$U(t)$$​ is [utilization rate](https://docs.orchai.io/orchai-money-market/borrowing#utilization-rate) and $$B(t)$$​ is[ borrow rate](https://docs.orchai.io/orchai-money-market/borrowing#borrowing-interest-rate) at time $$t$$ and $$r$$ is reserve factor.

{% hint style="info" %}
 Reserve factor is set at **10%**
{% endhint %}