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# Interest Rates

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