Formula and accounting assumptions
Periodic debt equals principal × (1 + nominal APR ÷ compounding periods per year) raised to periods per year × days ÷ 365. Simple debt is principal × (1 + APR × days ÷ 365), while continuous debt uses principal × exp(APR × days ÷ 365). Percentage inputs become decimal rates inside each formula. The effective annual rate uses the entered compounding frequency and a one-year horizon.
Worked hypothetical example
For $1,000 of debt at a nominal 10% rate over 730 days, annual compounding produces $1,210, including $210 of interest. Simple interest gives $1,200 because the first year's interest does not itself earn interest. Increasing the compounding frequency increases the balance for a positive nominal rate, approaching the continuous limit. At a zero rate, every version remains at principal, which provides a useful check on the units and the horizon.
Interpret the scenarios and limits
The model does not reproduce a specific lending protocol's index calculation. Variable rates, exact block timestamps, day-count conventions, integer approximations and repayments can change accrued debt. Sensitivity rows alter the rate while leaving principal and horizon fixed; they are separate scenarios, not a sequence of rate resets. Extremely large results are rejected instead of being displayed as infinite debt. Use this alongside collateral stress, since rising debt and falling collateral can affect health simultaneously.