Interest Rate Model

Veil uses a two-slope (kink) interest rate model — the same design used by Aave and Compound. Rates are low below the target utilization and increase steeply above it.

Borrow Rate Formula


utilization = total_borrows / total_deposits

if utilization ≤ optimal_utilization:
    borrow_rate = base_rate + slope1 × (utilization / optimal_utilization)
else:
    excess = utilization - optimal_utilization
    borrow_rate = base_rate + slope1 + slope2 × (excess / (1 - optimal_utilization))

Supply Rate Formula


supply_rate = borrow_rate × utilization × (1 - reserve_factor)

The reserve factor determines the fraction of interest that goes to the protocol treasury rather than to depositors.

Default Parameters

All rates are WAD-scaled (WAD = 1e18). The table shows human-readable percentages.

Parameter	Default Value	WAD value
`base_rate`	1% per year	`10_000_000_000_000_000`
`optimal_utilization`	80%	`800_000_000_000_000_000`
`slope1`	4% per year	`40_000_000_000_000_000`
`slope2`	75% per year	`750_000_000_000_000_000`
`reserve_factor`	10%	`100_000_000_000_000_000`

At 80% utilization (kink): borrow rate = 1% + 4% = 5%

At 100% utilization: borrow rate = 1% + 4% + 75% = 80%

Index-Based Accrual

Interest is accrued lazily at the start of every state-mutating instruction. Two global indices are maintained:


borrow_index(t) = borrow_index(t₀) × (1 + borrow_rate × Δt / SECONDS_PER_YEAR)
supply_index(t) = supply_index(t₀) × (1 + supply_rate × Δt / SECONDS_PER_YEAR)

Both indices start at WAD = 1e18 when the pool is initialised.

Depositor balance:


balance = shares × supply_index / WAD

Borrower current debt:


debt = principal × (borrow_index_current / borrow_index_at_borrow_time)

This means individual positions don’t need to be touched to stay up-to-date — the global index does the work. Depositors and borrowers earn/owe the correct amount regardless of when they last interacted.

Computing Rates Off-Chain


const WAD = 1_000_000_000_000_000_000n;
 
function utilizationRate(borrows: bigint, deposits: bigint): bigint {
  if (deposits === 0n) return 0n;
  return (borrows * WAD) / deposits;
}
 
function borrowRate(
  util: bigint,
  baseRate: bigint,
  optimalUtil: bigint,
  slope1: bigint,
  slope2: bigint,
): bigint {
  if (util <= optimalUtil) {
    return baseRate + (slope1 * util) / optimalUtil;
  }
  const excess = util - optimalUtil;
  return baseRate + slope1 + (slope2 * excess) / (WAD - optimalUtil);
}
 
function supplyRate(borrowRate: bigint, util: bigint, reserveFactor: bigint): bigint {
  return (borrowRate * util * (WAD - reserveFactor)) / WAD / WAD;
}