Level Perpetuity

Study guide: Exam FM-2

A level perpetuity is a Perpetuity with equal payments at every period, continuing forever. The present value of a perpetuity-immediate (payments at end of period) paying 1 per period at rate i:

a_{\overline{\infty}|} = \frac{1}{i}

• For a perpetuity-due (payments at start of period):

\ddot{a}_{\overline{\infty}|} = \frac{1}{d}

= \frac{1+i}{i}

• The present value formula follows from the limit of the finite annuity as n \to \infty, since v^n \to 0.
• Level perpetuities model preferred stock dividends, ground rents, and endowments.

Endowment Fund A university endowment must pay 50{,}000 annually (end of year) forever. At 5\% effective annual interest, how large must the endowment be?

Answer \text{PV} = \frac{50{,}000}{0.05} = 1{,}000{,}000