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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

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Core Calculation Function

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calculateInterest

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)

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Constants

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

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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.

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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.