Compound Amount Factor and Present Worth Factor identity: what is the product of CAF(S/P) and PWF(S/P) for the same interest rate and period count?

Introduction / Context:Engineering-economy factors come in inverse pairs. Understanding these dualities prevents algebra mistakes and speeds problem solving. The Compound Amount Factor from Present (often denoted F/P or CAF(S/P)) and the Present Worth Factor from Future (P/F or PWF(S/P)) are classic inverses.

Given Data / Assumptions:

• Interest rate i and period count n are the same for both factors.
• CAF(S/P) ≡ (1 + i)^n.
• PWF(S/P) ≡ 1 / (1 + i)^n.

Concept / Approach:By definition, a present amount P grows to F = P * (1 + i)^n; conversely, a future amount F discounts to P = F / (1 + i)^n. Multiplying the growth and discount factors cancels the compounding effect, returning the identity value 1. This property holds for any positive i and integer n (and indeed for real n under continuous compounding analogs with appropriately defined factors).

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