THE COMPOUNDING COST LAB
Frequency has a fee.
Compare what stays after every settlement.
A constant APR is an assumption, never a forecast.
01 Set the assumptions
Your experiment starts empty. Enter assumptions or load a synthetic example.
02 Compare the cadence
NO EXPERIMENT YETLet the intervals disagree.
Daily, weekly, 30-day, 90-day and annual settlement
will share the same assumptions. No live rates are loaded.
03 Follow every cash flow
Run a comparison to inspect the ledger or export a reproducible workbook. You can also import a saved experiment.
PUBLISHED MODEL / V1
A recurrence you can inspect.
Balance grows at a constant nominal annual rate between settlements. The fixed operation fee leaves immediately after interest is added.
a = APR ÷ 100; Δ = days in this period; f = fee in the same units as principal. The recurrence applies only when the accrued balance can pay the fee.
What happens at the boundary?
If accrued balance is less than the fee, retain it, record the unpaid fee and stop. If a paid fee leaves zero, stop. Net result can be negative without creating a negative balance.
Closed form & break-even
For n equal periods, q = 1 + aΔ/365:
Bₙ = Pqⁿ − f(1 + q + … + qⁿ⁻¹).
When a = 0, Bₙ = P − nf.
For mixed period lengths, carry A ← Aq and C ← Cq + 1, starting at A = 1, C = 0. Then B = AP − Cf and the principal break-even fee is P(A − 1)/C. A negative threshold means no nonnegative fee preserves principal.
What this experiment leaves out
No changing rates, taxes, slippage, price movements, real yield pools, automatic reinvestment or APY promise. All currency units are generic. This model is a mathematical scenario, not an investment recommendation.