Present Value (Lump Sum) mechanism

Model scope

The mathematical formula is standard under nominal annual-rate and periodic-compounding assumptions, but the specification needs to explicitly define the rate convention, input units, valid ranges, and discount-factor definition. The honest label Educational estimate is appropriate if those assumptions and rounding behavior are shown to users.

• PV=FV/(1+r/n)^(nt) is the standard formula only when rate is a nominal annual rate expressed as a decimal and compounded n times per year.
• The specification does not define whether the reported discount factor means PV/FV; the formula implies discount factor=(1+r/n)^(-nt).
• The formula is not correct if rate is already an effective annual rate, a periodic rate, or a continuously compounded rate.

Units and conventions

• FV and PV use the same currency units.
• rate is a nominal annual percentage represented as a decimal, so 5% must be entered as 0.05.
• compounds/yr is a positive integer n.
• years is measured in years and may be fractional; nt is the total number of compounding periods.
• The discount factor is dimensionless and defined as PV/FV=(1+r/n)^(-nt).

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "FV": 10000,
    "rate": 0.05,
    "compounds_per_year": 4,
    "years": 3
  },
  "expected_outputs": {
    "PV": 8615.09,
    "discount_factor": 0.8615086
  },
  "working": "r/n=0.05/4=0.0125. nt=4*3=12. 1+r/n=1.0125. (1.0125)^12=1.1607545177. discount factor=1/1.1607545177=0.8615086. PV=10000*0.8615086=8615.086, which rounds to 8615.09."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The formula reaches an undefined division-by-zero result when rate = -compounds_per_year, and the specification does not state validation or rejection behavior. Rate-unit ambiguity can also change the result by a large factor.

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-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json