Source: https://guthlabs.ai/docs/instruments/present-value-lump-sum/

instrument / verified-clean

# Present Value (Lump Sum)

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/present-value-lump-sum/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/present-value-lump-sum/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/present-value-lump-sum/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/present-value-lump-sum/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Finance, Economics & Business

**Tranche**: tranche-2

**Evidence ID**: t2-008

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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).

## Boundary hardening

**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.

## 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": {
    "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."
}
````

## 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_CLEAN`

- `evidence-tranche2/tranche2-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`