# Borrowing

Each pair gives the opportunity for users to borrow Asset Tokens, in return borrowers must supply the Pair with the appropriate amount of Collateral Tokens

As long as borrowers have an open position, interest accrues and is capitalized. This means that over time the amount a borrower owes increases by an amount equal to the interest they owe. In order for a borrower to receive their collateral back, they must return the original loan amount plus all accrued interest.

### A Borrowing Example

Just like we used the Asset Vault Account to keep track of the total asset amounts and the corresponding number of shares, we use the Borrow Vault Account to keep track of the total amount borrowed, the capitalized interest, and the number of outstanding borrow shares.

Suppose that Alice has borrowed 100 FRAX ($100 of value) using $150 worth of ETH. Since her initial borrow she has accumulated 10 FRAX of interest. The Borrow Vault Account would appear as follows:

Borrow Vault Account | Total |
---|---|

Amount | 110 FRAX |

Shares | 100 |

Alice Collateral Amount | $150 ETH |

Alice Borrow Shares Balance | 100 |

Remember that borrower's positions must remain below the Maximum Loan-To-Value (LTV). Because Alice's LTV is 73.33% she is below the max value of 75% and her position is considered healthy.

We calculate Alice's LTV in the following way. First we calculate the value of her loan to be $110 by multiplying her Borrow Share Balance (100 shares) by the Borrow Share Price (1.10), then multiply by the FRAX price given in USD (1.00). The value of her loan is $100 (100x1.10x1.00). The value of her collateral is $150. This gives $110 / $150 = 73.33%

Bob now borrows 100 FRAX, using $175 worth of ETH. Given the current Borrow Share Price of 1.10, his Borrows Shares Balance would be approximately 90.91. Unlike lenders, borrowers do not receive an ERC20 token representing their debt, instead the Share Balances are simply stored in the Pair. Now the Borrow Vault Account looks like this:

Borrow Vault Account | Total |
---|---|

Amount | 210 FRAX |

Shares | 190.91 |

Alice Collateral Amount | $150 ETH |

Alice Borrow Shares Balance | 100 |

Bob Collateral Amount | $175 ETH |

Bob Borrow Shares Balance | 90.91 |

Suppose that the Pair accrues another 20 FRAX of interest. The Borrow Vault Account now looks like this:

Borrow Vault Account | Total |
---|---|

Amount | 230 FRAX |

Shares | 190.91 |

Alice Collateral Amount | $150 ETH |

Alice Borrow Shares Balance | 100 |

Bob Collateral Amount | $175 ETH |

Bob Borrow Shares Balance | 90.91 |

The new Borrow Share Price is 1.2048 (230 / 190.91). This means that in order for Alice to repay her debt she will need to repay 120.48 FRAX (Alice Shares (100) x Share Price (1.2048)). Likewise, Bob would need to repay 109.52 FRAX (Bob Shares (90.91) x Share Price (1.2048)).

As interest accrues the amount required to repay the loan increases and the LTV of each position changes.

Alice's LTV: 80.32% (120.48 / 150)

Bob's LTV: 62.58% (109.52 / 175)

As the interest accrued and was capitalized, Alice's position has entered an unhealthy state as her LTV is above the Maximum LTV of 75%. This puts her at high risk of having her position liquidated.

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