Finance (FINC) Test 2 Practice

For a perpetuity that pays a fixed amount every year forever, the present value comes from summing all discounted future payments. The value today is the sum C/(1+r) + C/(1+r)^2 + C/(1+r)^3 + …, which is a geometric series. The infinite sum of this series equals C/r, so the present value is C divided by the discount rate r. An intuitive way to see it: if you invest P today at rate r, you earn P*r each year. To fund perpetual payments of C, the annual payout must equal the earning, so P*r = C, giving P = C/r. So the correct expression is PV = C/r. The other forms don’t fit: multiplying by r would imply the value grows with the rate rather than being discounted; discounting just the next payment gives C/(1+r), not the infinite stream; multiplying by (1+r) inflates beyond the present value.