Ordinary Annuity FV/PV mechanism

Model scope

The ordinary-annuity formulas are standard under the stated unit and timing assumptions, but the instrument specification is ambiguous because it advertises an annuity-due toggle without supplying or explicitly requiring the due formulas. It also lacks a defined zero-rate branch. Resolve those behaviors before claiming the instrument is fully formula-verified.

• The FV and PV formulas are correct for an ordinary annuity with equal payments made at the end of each period, provided r is nonzero.
• The specification includes an annuity-due timing toggle, but neither formula includes the required due adjustment: FV_due=FV_ordinary*(1+r) and PV_due=PV_ordinary*(1+r).
• The formulas divide by r and therefore do not directly handle a zero rate; the correct zero-rate limit is FV=PMT*n and PV=PMT*n.
• The formulas do not state constraints such as n being a nonnegative integer and r being greater than -1 for standard real-valued discounting.

Units and conventions

• r is a decimal rate per payment period, not an annual rate unless payments are annual; for a nominal annual rate with m payments per year, use r=annual_rate/m.
• n is the total number of payment periods and must be a nonnegative integer.
• PMT is the equal payment amount per period; signs must be defined consistently for cash-flow convention.
• Ordinary annuity payments occur at the end of each period.
• The test-vector growth value is defined as FV minus total contributions, where total contributions=PMT*n.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "PMT": 1000,
    "rate_per_period": 0.05,
    "n": 3,
    "timing": "ordinary"
  },
  "expected_outputs": {
    "FV": 3152.5,
    "PV": 2723.248029,
    "total_contributions": 3000,
    "FV_growth": 152.5
  },
  "working": "FV=1000*((1.05)^3-1)/0.05=1000*(1.157625-1)/0.05=1000*0.157625/0.05=3152.50. PV=1000*(1-(1.05)^(-3))/0.05=1000*(1-0.8638375985)/0.05=1000*0.1361624015/0.05=2723.248029. Total contributions=1000*3=3000. FV growth=3152.50-3000=152.50."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The formulas require domain and convention handling that is not explicit: zero-rate handling needs a limiting implementation, r=-1 makes PV undefined, and an unlabelled rate value such as 5 produces radically different results depending on whether it means 5% or decimal 5.

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