ROI Calculator mechanism

Model scope

The educational-only and not-investment-advice label is appropriate. Before release, rename or define "gain" explicitly as final_value, document that annualized ROI means CAGR, and enforce initial_cost>0, holding_period_years>0, and final_value>=0 for real-valued annualization.

• The input list provides initial cost and final value, but the formula uses an undefined variable named "gain". The standard formula with these inputs is ROI=(final_value-initial_cost)/initial_cost. The supplied formula is correct only if "gain" actually means final value, which is nonstandard terminology; if gain means profit, the supplied formula is incorrect.
• The annualized formula is a valid compound annual growth rate (CAGR) formula for one initial outflow and one final value: (1+ROI)^(1/years)-1. It is not a general annualized return formula for investments with interim cash flows or contributions.
• The specification does not state the required domain constraints initial_cost>0 and years>0, nor that final_value must be nonnegative for a real-valued annualized result.

Units and conventions

• Initial cost and final value must use the same currency and price basis; currency conversion is not performed.
• Holding period is measured in years. For a six-month period, years must be entered as 0.5, not 6.
• ROI and annualized ROI are computed internally as decimal rates and displayed as percentages by multiplying by 100.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "initial_cost": 1000,
    "final_value": 1200,
    "holding_period_years": 2
  },
  "expected_outputs": {
    "roi_percent": 20,
    "annualized_roi_percent": 9.544511501
  },
  "working": "ROI=(1200-1000)/1000=200/1000=0.20=20%. Annualized ROI=(1+0.20)^(1/2)-1=1.20^0.5-1=1.095445115-1=0.095445115=9.544511501%."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

An initial cost of zero makes the ROI denominator vanish, producing an undefined result. The specification does not state an input-validation rule, so the calculator must explicitly reject this case rather than emit Infinity or NaN.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json