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

# Math Reference

> WAD, shares, kink rates, health, and liquidation formulas from the Solana program.

Source: `programs/vanna_lending/src/math/`.

## Scales

```text theme={null}
WAD                  = 10^18
USD_VALUE_DECIMALS   = 9
BASIS_POINTS         = 10_000
SECONDS_PER_YEAR     = 31_536_000
BALANCE_TO_BORROW    = 1.1 × WAD
CLOSE_FACTOR_BPS     = 5_000
MIN_INITIAL_SHARES   = 1_000
```

## Utilization and kink rate

```text theme={null}
u_bps = floor(borrows × 10_000 / (cash + borrows))

if u ≤ u_opt:
  rate_bps = base + floor(slope1 × u / u_opt)
else:
  rate_bps = base + slope1 + floor(slope2 × (u − u_opt) / (10_000 − u_opt))
```

## Accrual

```text theme={null}
interest = ceil(total_borrow × rate_bps × elapsed / (10_000 × SECONDS_PER_YEAR))
fee      = floor(interest × reserve_factor_bps / 10_000)
total_borrow' = total_borrow + interest
fees'         = fees + fee
index'        = index × (total_borrow' / total_borrow)   // WAD
```

Reject `now < last_update` (`TimestampRegression`).

## Lender shares

```text theme={null}
lender_assets = cash + borrows − fees

supply_shares = floor(assets × total_shares / lender_assets)   // 1:1 if empty
redeem_assets = floor(shares × lender_assets / total_shares)
```

## Debt shares

```text theme={null}
new_shares  = ceil(assets × total_borrow_shares / total_borrow_assets)  // 1:1 if empty
user_debt   = ceil(user_shares × total_borrow_assets / total_borrow_shares)
repay_share = floor(paid × total_borrow_shares / total_borrow_assets)
```

Borrow shares round **up**. Lender shares and redeem assets round **down**.

## USD and health

```text theme={null}
value = token_amount × price × 10^(exp − decimals + 9)
HF    = collateral_usd / debt_usd
ok    ⇔ HF > 1.1
```

Collateral value floors. Debt value ceils. `value_to_token_amount` is the inverse used by liquidation seize.

## Liquidation seize

```text theme={null}
repay    ≤ 50% of that debt   // CLOSE_FACTOR_BPS = 5_000
seize_usd = repay_usd × (10_000 + bonus_bps) / 10_000
seize_tok = value_to_token_amount(seize_usd, …)
```

Require `seize_tok ≥ min_collateral_out`.

`CLOSE_FACTOR_BPS` is a compiled constant, not a governed `Reserve`/`ProtocolConfig` field. The code comment above it explicitly calls the 50% figure illustrative — "requiring simulation and audit before production, not a frozen protocol parameter" — so treat it as a V1 default, not a permanent guarantee.