Source: https://guthlabs.ai/docs/instruments/ordinary-annuity-fv-pv/
instrument / verified-with-binding-errata
# Ordinary Annuity FV/PV
The current ledger marks this instrument verified with errata that must be applied at binding time.
Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified with errata that must be applied at binding time.
**Area**: Finance, Economics & Business
**Tranche**: tranche-2
**Evidence ID**: t2-020
**Ledger rows**: 1
No ledger note is attached.
## Review findings
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.
### Formula and scope findings
- 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.
### Unit assumptions
- 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.
## Boundary hardening
**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.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"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."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA`
- `evidence-tranche2/tranche2-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`