Interest rates

## Utilization rate

All interest rates in Drops are determined as a function of a metric known as the utilization rate. The utilization rate
$U_a$
for a money market
$a$
is defined as:
$U_a = Borrows_a / (Cash_a + Borrows_a - Reserves_a)$
• $Borrows_a$
refers to the amount of
$a$
borrowed.
• $Cash_a$
refers to the amount of
$a$
left in the system.
• $Reserves_a$
refers to the amount of
$a$
that Drops keeps as profit.
Intuitively speaking, this is the percentage of money borrowed out of the total money supplied.

## Borrow & Supply rates

The borrowing rate's calculation depends on something called an interest rate model - the algorithmic model to determine a money market's borrow and supply rates.
Borrow and supply rates are calculated using the utilization rate and several arbitrary constants.
Markets follow what is known as the "Jump Rate" model, which contains the following parameters:
• Base rate per year - the minimum borrowing rate
• Multiplier per year - the rate of increase in interest rate with respect to utilization
• Kink - the point in the model in which the model follows the jump multiplier
• Jump Multiplier per year - the rate of increase in the interest rate with respect to utilization after the "kink"
The borrow rate of the jump rate model is defined as follows:
\begin{aligned} \text{Borrow Interest Rate} &= \text{Multiplier} * min(U_a, \text{Kink}) \\ &+ \text{Jump Multiplier} * max(0, U_a - \text{Kink}) \\ &+ \text{Base Rate} \end{aligned}

## Example

The USDC rate model is a jump rate model with the following parameters:
• Base rate: 0%/yr
• Multiplier: 5%/yr
• Kink: 80%
• Jump multiplier: 109%/yr
• USDC market reserve factor: 7%.
Let's say that the market has the following status:
• $180M in borrows •$20M in cash
What is the borrow rate and supply rate?
Doing the math:
$U_a = \180M/(\180M + \20M) = 90\%$
$\text{Borrow Interest Rate} = 5\% * 80\% + 109\% * (90\% - 80\%) + 0\% = 14.9\%$
$\text{Supply Interest Rate}_a = 14.9\% * 90\% * (1 - 7\%) = 12.5\%$