# Interest Rates

Not arbitrarily defined by a central entity, but by pure mathematics.

Finny has three important values used to calculate accurate interest rates - the utilization rate, supply rate and borrow rate.

## Utilization Rate

The utilization rate of a market is the ratio between total borrowed assets and total lent assets - think of it as the percentage of used assets in a market. It is the core of the interest rate model.

The utilization rate $R$ of a market $x$ can be formally defined as

$R_x=Borrowed_x/(Supplied_x+Borrowed_x−Reserves_x)$. Reserves being, the total amount that Finny currently has as profit (more on this later).

## Borrow Rate

The supply rate of a market is the interest of borrowers paid yearly. That is, the delta borrowers have to include when repaying an open position.

It can be formally defined as: $B_x=Mul_x ∗ R_x+Base_x$

$Mul_x$ refers to the multiplier of a market - which is the rate of increase in interest rate in regards to the utilization.

$R_x$ being the utilization rate of market $x$.

$Base_x$ refers to the base rate of a market - the ever possible minimum borrowing rate.

So for example, there are 1000 BTC supplied, and 100 BTC borrowed, which gives us a 10% utilization rate, the multiplier for BTC is set at 20% and the base rate at 5%. The borrow rate for BTC would be 7%, seen as follows:

$B_x = 0.2 * 0.1 + 0.05 = 0.07$

## Supply Rate

The supply rate is the yield (or APY) that is given to suppliers. The supply rate $S$ of market $x$ is defined as follows:

$S_x = B_x * R_x *(1 - Rf_x)$

$B_x$ is the borrow rate of the market.

$R_x$ is the utilization rate of the market.

$Rf_x$ being the reserve factor of the market - the percentage of the delta between $S_x$ and $B_x$ that Finny stores as profit.

Let's go through a scenario using the same market as in the borrow rate (BTC) - it has a 10% utilization rate, the borrow rate is 7% and the reserve factor is set to 15%. The supply rate would be 0.59%, calculated as follows:

$S_x = 0.07 * 0.1 * (1 - 0.15)$

### How is interest accrued?

Borrow interest is accrued each time there is a successful call of any of the following methods:

`Borrow()`

`Mint()`

`Repay()`

`Redeem()`

These methods all alter the ratio of assets in the protocol.

As such, the rates are ever-changing, and the really attractive supply rate that you are obtaining today can fluctuate heavily depending on large movements between the borrowed and supplied assets.

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