# Deposit Rate Subsidization

Anchor Protocol's deposit rate stability is supported by borrow demand from borrower ANC distribution and direct subsidization. Anchor defines a target deposit rate ($r_{target}$), and a threshold deposit rate ($r_{threshold}$) and constantly attempts to retain a deposit rate close to $r_{target}$ and always above $r_{threshold}$.

Every epoch, the average deposit rate during the last epoch ($r_{current}$) is calculated and compared with the target and threshold rates. Appropriate measures are then made to readjust the deposit rate.

## Borrower ANC Incentives

Anchor's deposit rate is primarily adjusted by calibrating the rate of ANC emission to borrowers ($e$), updated through a feedback control algorithm.

### ANC Emission Feedback Control

Anchor alters the ANC emission rate based on a **multiplicative increase / multiplicative decrease feedback control** algorithm, which adjusts the ANC emission rate of the next epoch $e_{n+1}$ based on the previous emission rate of $e_n$:

$$
e_{n+1} = k \cdot e_n
$$

The feedback control algorithm adjusts incentives with $r_{average}$ - the average of $r_{target}$ and $r_{threshold}$ - as the reference point:

$$
r_{average}=\frac{r_{target}+r_{threshold}}{2}
$$

* If deposit rate is approaching the threshold ($r_{current} < \frac{r_{threshold}+r_{average}}{2}$), increase emission by 0.7% ($k \approx 1.007$)
* If deposit rate approaches the target ($r_{current} > \frac{r_{target}+r_{average}}{2}$), reduce emission by 0.3% ($k \approx 0.997$)

where the set $k$ values result in a 50% emission increase over a week-long period or a 15% decrease over a week-long period.

## Direct Subsidization

As an additional layer of safety, the protocol directly subsidizes the deposit rate if it is below the threshold rate ($r_{current}<r_{threshold}$), funded from the yield reserve's stockpiled stablecoins.&#x20;

An amount required to raise the deposit rate to the threshold is distributed to depositors, which is limited to 10% of the yield reserve's balance per subsidization to prevent excessive drainage. Distributed subsidies are added to the money market’s liquidity, increasing the aTerra exchange rate and appreciating the value of aTerra.