# Borrow APY

Users who borrow pay interests to a market (for the users who supply). The interest is  compounded with every new block that appears on the blockchain, so the debt increases every minute. 

Both Borrow Rate (APR) and Borrow APY of an asset on a specific market are not fixed, but depend on the current utilization of the asset:

$$
U = UtilizationRate = \frac{AmountBorrowed}{AmountSupplied}
$$

* When the asset is available, interests are low to encourage borrowing.
* When the asset is scarce: interests are high to encourage repayments of debt and additional supplying.

The difference is that Borrow APY takes into account compound interest, and Borrow Rate does not.

The graph of APR and APY dependence on Utilization Rate looks like this:

<figure><img src="/files/hvKNxRzqaVrQLPOqU7fa" alt=""><figcaption></figcaption></figure>

## Borrow Rate

Borrow Rate (annual percentage rate, APR) refers to the yearly interest paid by borrowers does not take compounding into account.

The Borrow Rate function is split in two parts around an optimal utilization rate $$U\_{opt}$$​:

$$
BorrowRate = \begin{cases}
R\_0+\frac U{U\_{opt}}R\_{slope1} ,\&if\ U\<Uopt\newline R\_0+R\_{slope1}+\frac{U-U\_{opt}}{1 -U\_{opt}}R\_{slope2},\&if\ U\ge Uopt
\end{cases}
$$

Where $$R\_0$$, $$R\_{slope1}$$, $$R\_{slope2}$$ are asset parameters.

## Borrow APY

Your borrowed amount grows with every new block due to compounding. Borrow APY (annual percentage yield) refers to the yearly interest paid by borrowers, taking into account the effect of compounding.

Borrow APY is calculated as follows:

$$
BorrowAPY = \bigg(1 + \frac{BorrowRate}{BlocksPerYear}\bigg)^{BlocksPerYear} - 1
$$

A new block is added to the Waves blockchain about once a minute, so

$$
BlocksPerYear = 365\cdot 24\cdot 60 = 525,600
$$


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