> ## Documentation Index
> Fetch the complete documentation index at: https://docs.monolith.market/llms.txt
> Use this file to discover all available pages before exploring further.

# InterestModel

> Dynamic interest rate calculation for borrowing

# Interest Model

The InterestModel contract calculates the borrow rate and accrued interest using an exponential controller driven by the free‑debt ratio. It is a shared, pure math contract used by all `Lender` instances.

[Contract implementation](https://github.com/MonolithMarket/Monolith/blob/main/src/InterestModel.sol)

## Core Calculation Function

### calculateInterest

```solidity theme={null}
function calculateInterest(
    uint _totalPaidDebt,
    uint _lastRate,
    uint _timeElapsed,
    uint _expRate,
    uint _lastFreeDebtRatioBps,
    uint _targetFreeDebtRatioStartBps,
    uint _targetFreeDebtRatioEndBps
) external pure returns (uint currBorrowRate, uint interest)
```

Calculates the new borrow rate and the interest accrued over `_timeElapsed` seconds using an exponential controller around a target free‑debt ratio band.

**Parameters:**

* `_totalPaidDebt`: Current paid (interest‑bearing) debt principal `D`.
* `_lastRate`: Previous borrow rate mantissa `r_old` (APR scaled by 1e18).
* `_timeElapsed`: Seconds since last accrual `dt`.
* `_expRate`: Exponential rate constant `k` (derived from half‑life via `wadLn(2e18)/halfLife`).
* `_lastFreeDebtRatioBps`: Last observed free‑debt ratio `f` in basis points (0–10000), including PSM assets.
* `_targetFreeDebtRatioStartBps`, `_targetFreeDebtRatioEndBps`: Target band `[f_start, f_end]` in basis points.

**Returns:**

* `currBorrowRate`: Updated borrow rate mantissa `r_new` (APR scaled by 1e18).
* `interest`: Accrued interest amount over the interval.

**Algorithm summary:**

* Let `g = exp(-k * dt)`.
* If `f < f_start` (below band): rate grows exponentially
  * `r_new = r_old / g`
  * `interest = D * (r_new - r_old) / (k * 365 days)`
* Else if `f > f_end` (above band): rate decays exponentially toward a floor
  * `r_new = max(r_old * g, r_min)` with `r_min = 0.5% APR`
  * If the decay hits the floor during `dt`:
    * `t_min = -ln(r_min / r_old) / k`
    * `interest = D * ((r_old - r_min) / k + r_min * (dt - t_min)) / (365 days)`
  * Else:
    * `interest = D * (r_old - r_new) / (k * 365 days)`
* Else (inside band): hold rate constant
  * `r_new = r_old`
  * `interest = D * r_old * dt / (365 days * 1e18)`

## Constants

* `MIN_RATE = 0.5% APR` (as `5e15` in 1e18 mantissa) — lower bound for the borrow rate.

## Integration Notes

* The model is stateless and pure; it is called externally by `Lender` using `try/catch` so accrual can safely skip if anything unexpected happens.
* Each `Lender` stores its own `expRate` (set via half‑life) and target band; these can be adjusted before the immutability deadline.
* One shared `InterestModel` instance is deployed by the `Factory` and referenced by all `Lender` contracts.

## Security Considerations

* Pure math (no state) and no external calls inside the function.
* Uses wad math (`wadExp`, `wadLn`) and explicit floor handling to avoid overflows and negative rates.