# Interest Model

In the money market of each individual asset, Aptin balances the interest rate automatically based on the assets supply relationship (funding utilization rate). The suppliers and borrowers do not need to negotiate terms and interest rates individually since the Aptin has an interest rate model implemented. The utilization rate ***U*** for each money market ***a*** unifies the asset supply and demand relationship into one variable:

$$
\mathit{U\_{a}=\frac{\text { Borrows }*{a}}{\left(\text { Cash }*{a}+\text { Borrows }\_{a}\right)}}
$$

***borrows\_a*** represents the outstanding loan balance in the money market ***a***; ***Cash\_a*** represents the balance of assets supplied to the money market ***a***. Subjecting to economic principles, when borrowing demand is low, interest rates should be low; on the contrary, when borrowing demand is high, interest rates should rise. The borrowing demand is expressed by the utilization rate function. <br>

The current set borrowing interest rate (***BorrowInterestRate\_a***) is obtained from the utilization rate and a ***BaseInterestRate\_a*** of ***B***, ***InterestRateGrowthFactor\_a*** is ***K***：

$$
\mathit{\text { BorrowInterestRate }*{a}=\left(K*{a} \* U\_{a}+B\_{a}\right){\normalsize \mathit{} } }
$$

Supply interest rate is calculated based on the Borrower interest rate.

$$
\mathit{\text { SupplyInterestRate }*{a}=\left(BorrowInterestRate \_ { a } \* U*{a}\right){\normalsize \mathit{} } }
$$

Within one money market ***a***, there is the following interest rate equilibrium:

$$
\mathit{\text { Borrows }*{a} \* \text { BorrowingInterestRate }*{a}=\text { Supplies }*{a} \* \text { SupplyInterestRate }*{a}}
$$

The figure below shows the interest rate change influenced by the utilization rate, where the fund utilization rate is 0, the borrowing rate is 0.0253 and the deposit rate is 0：

<figure><img src="/files/CEicYS1vlg88tgpk5tgE" alt=""><figcaption><p><em>Interest Rate Change</em></p></figcaption></figure>


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