> anishgoyal █


Notes › MATH 5441: Financial Mathematics Lecture 18

Perpetuities

calendar_today   article 111 words   access_time 1 min   replay Modified

Table of Contents

Perpetuity

$$a_{\left< \infty \right> } = \lim_{ n \to \infty } a_{\left< n \right> } = \lim_{ n \to \infty } \frac{1 - (1 + i)^{-n}}{i} = \frac{1}{i}$$ $$\ddot a_{\left< \infty \right> } = \lim_{ n \to \infty } \ddot a_{\left< n \right> } = (1+i) \lim_{ n \to \infty } \frac{1 - (1 + i)^{-n}}{i} = \frac{1+i}{i}=\frac{1}{d}$$

perpetuity example problem

Perpetuity second example problem

Graph

mindmap ↗