# Accrued Interest Calculation

### Formulae

<details>

<summary><strong>Interest = (r * x * t) / 1yr / 10000</strong></summary>

r = APR in basis points (e.g. 5% = 500bp)

x = amount of tokens

t = time (in seconds)

1 year = 365.25 days (in seconds)

</details>

<details>

<summary>Full Accrued Interest formula</summary>

`InterestAccrued =`

`(rate.dRate * drawnBalance * timespan) / INTEREST_DENOMINATOR`

`+`

`(rate.fRate * (facilityBalance - drawnBalance) * timespan) / INTEREST_DENOMINATOR`

</details>

### Parameters

<details>

<summary>interestAccrued</summary>

Interest owed by a Borrower but not yet repaid to the Line of Credit contract

</details>

<details>

<summary>Interest denominator = 365.25 days * Base denominator</summary>

</details>

<details>

<summary>Base denominator</summary>

10000 (adjustment factor since rates are expressed in basis points (bps) --> e.g. 5% rate is expressed as 500bp so we need to divide by 100 to get a % and then by another 100 to arrive at the decimal (500/100/100 = 0.05)

</details>

<details>

<summary>One year</summary>

One Julian astronomical year, has 365.25 days: 1 year = 365.25 days = (365.25 days) × (24 hours/day) × (3600 seconds/hour) = 31557600 seconds

</details>

<details>

<summary>dRate</summary>

The annual interest rate charged to a Borrower on borrowed / drawn down funds (in basis points to 4 decimals, e.g. 1000bp = 10% and 1234bp = 12.34% and 1234.56bp = 12.3456%)

</details>

<details>

<summary>drawnBalance</summary>

The balance of funds that a Borrower has drawn down on the Line of Credit

</details>

<details>

<summary>fRate</summary>

The annual interest rate charged to a Borrower on the remaining funds available, but not yet drawn down aka rate charged on the available facility headroom(in basis points to 4 decimals).

</details>

<details>

<summary>facilityBalance</summary>

The remaining balance of funds that a Borrower can still drawn down on the Line of Credit (aka headroom)

</details>

<details>

<summary>timespan= block.timestamp - rate.lastAccrued</summary>

The number of seconds for which interest will be accrued

</details>

<details>

<summary>block.timestamp</summary>

The block timestamp for the block during which interest is calculated, in seconds

</details>

### Contract workflow

Please see [here](/developer-material/v1-developer-material/functions-and-methods/interestratecredit.sol/interest-accrued-contract-flow.md) for an overview of the contract and function workflow.

The definitions below are useful for that.

<details>

<summary>Principal</summary>

The amount of a Lender's Deposit that has actually been drawn down by the Borrower (USD)

</details>

<details>

<summary>Deposit</summary>

The sum of the total liquidity provided by a Lender in a given token on a Line of Credit

</details>

<details>

<summary>id</summary>

Reference id for the Credit Position made available to a Borrower by a single Lender for a given token on a Line

</details>


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