The specification travels with the result

Each supported model defines the decision, symbols, units, sign convention and timing before a calculator is allowed to return a number.

Model version: 2026-08-17.finance-lab.1. These specifications cover the current review artifact and change whenever a formula, timing rule, numerical method or input meaning changes.

compound-interest

Project a balance under a stated nominal annual rate and contribution schedule

Symbols

P: initial principal; unit: currency
C: contribution each contribution period; unit: currency per contribution period
j: nominal annual rate; unit: decimal per year
m: compounds per year; unit: whole periods per year
p: contributions per year; unit: whole periods per year
n: number of contribution periods; unit: periods

Sign convention: principal and contributions are non-negative deposits

Timing: contributions occur at the beginning or end of each contribution period

break-even

Find the sales volume at which contribution margin covers fixed cost

Symbols

F: fixed costs; unit: currency per decision period
P: selling price per unit; unit: currency per unit
V: variable cost per unit; unit: currency per unit
Q: break-even units; unit: units per decision period

Sign convention: costs and prices are non-negative

Timing: all inputs use the same operating period

npv-irr

Compare periodic or dated cash flows with an explicit discount rate or return root

Symbols

CF_t: cash flow at period or date t; unit: currency
r: discount rate per period or annual dated rate; unit: decimal
t: period number or year fraction; unit: period or ACT/365 year fraction

Sign convention: outflows are negative and inflows are positive

Timing: periodic NPV starts at t=0; dated XNPV uses actual dates divided by 365

financial-ratios

Relate two explicitly defined financial-statement or investment fields

Symbols

N: named numerator; unit: currency or units
D: named denominator; unit: matching currency or units

Sign convention: negative denominators remain visible and zero denominators are undefined

Timing: numerator and denominator must use the stated period and ending or average balance basis

Shared failure rule

Invalid, undefined, period-mismatched, non-convergent and ambiguous states are named. The engine does not convert one of those states into zero, an empty result or a plausible-looking rate.

Numerical scope

The current IRR and XIRR routine scans from −99.9% through 1,000%, brackets sign changes and refines each root. It reports no solution or multiple roots within that supported range. That is a stated numerical boundary, not a proof that no other mathematical root exists outside the range.