fix(utils): apply the min deposit rate to interest calculations

[pucedoteth]

The bug

min_deposit_rate_x18 is parsed into SpotProductConfig:

class SpotProductConfig(NadoBaseModel):
    ...
    min_deposit_rate_x18: str

and then never read anywhere in the SDK. Neither calc_borrow_rate_in_period nor calc_deposit_rate_in_period applies it, so both under-report against what the engine actually accrues.

SpotEngine._updateState converts the rate to a per-second figure, compounds it over dt, and multiplies the result into both multipliers:

int128 minDepositRatePerSecondX18 = minDepositRateX18.div(MathSD21x18.fromInt(31536000));
int128 minDepositRateMultiplierX18 = (ONE + minDepositRatePerSecondX18).pow(int128(dt));

state.cumulativeBorrowsMultiplierX18  = state.cumulativeBorrowsMultiplierX18.mul(minDepositRateMultiplierX18);
state.cumulativeDepositsMultiplierX18 = state.cumulativeDepositsMultiplierX18.mul(minDepositRateMultiplierX18);

With a 5% min deposit rate, a 3.5% borrow curve and 50% utilization:

period	SDK	engine
1 hour	3.995e-06	9.703e-06
1 day	9.590e-05	2.329e-04
30 days	2.881e-03	7.011e-03

The same problem on the deposit side

calc_deposit_rate_in_period returns 0 when nothing is borrowed:

utilization = calc_utilization_ratio(product)
if utilization == 0:
    return 0

On chain, zero utilization only zeroes the borrower rate — borrowerRateX18 = 0. The minDepositRate block runs regardless and multiplies the deposit multiplier, so depositors still earn the floor while the pool is idle, which is the purpose of a rate floor.

The fix

calc_min_deposit_rate_multiplier reproduces the engine's minDepositRateMultiplier, and both functions apply it multiplicatively the way _updateState does.

The rate is read from product.config, which these functions already receive — the same way calc_borrow_rate_per_second already reads interest_floor_x18 and friends — so there are no signature changes and nothing downstream breaks.

_calc_borrow_multiplier was split out because the deposit rate is derived from the engine's borrowRateMultiplier before the min deposit multiplier is applied; reusing calc_borrow_rate_in_period there would apply the floor twice.

Companion change

The TypeScript SDK has the mirror image of this bug — it adds the annual rate to the period rate instead of omitting it, so it over-reports where this one under-reports. That is nadohq/nado-typescript-sdk#452. After both, the two SDKs agree with the engine and with each other.

Test plan

tests/utils/test_interest.py adds 7 cases pinned to the engine's formula rather than to current output, across an hour, a day, 30 days and a year, plus the idle-pool deposit case.

Reverting only interest.py and keeping the tests fails with the table above:

Obtained: 3.995441563597879e-06     (1 hour, SDK)
Expected: 9.703242916270227e-06     (1 hour, engine)

Obtained: 9.589500359430403e-05     (1 day, SDK)
Expected: 0.0002329038180453047     (1 day, engine)

pytest tests/        # 254 passed
black --check        # 2 files would be left unchanged

ruff check reports I001 (unsorted import block) on nado_protocol/utils/interest.py, but it does so on a clean checkout too — the import block is untouched here, so I left it rather than mixing an unrelated reorder into this diff.

[claude]

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