Finance (FINC) Test 1 Practice 2026 - Free Finance Practice Questions and Study Guide

The key idea is valuing a stream of identical payments that continues forever. Each payment is worth less today because of time value, so you sum the present value of every future payment: PMT/(1+r) + PMT/(1+r)^2 + PMT/(1+r)^3 + … to infinity. This is a geometric series with first term PMT/(1+r) and common ratio 1/(1+r). The sum of such a series is [first term] / [1 − ratio] = [PMT/(1+r)] / [1 − 1/(1+r)] = [PMT/(1+r)] / [r/(1+r)] = PMT / r. So the present value of a perpetuity paying PMT each year forever is PMT divided by the discount rate.

Why the other forms don’t fit: multiplying PMT by r fails to capture the time-value of the entire infinite stream. Using PMT × (1 + r) ignores discounting of future payments and overstates value. The expression PMT × (1 − r)/r resembles a finite-period annuity formula, but the proper finite-n form is PMT × [1 − (1 + r)^−n] / r, which approaches PMT/r as n grows large, not the given form.