Textbook Problem

Annuities If an annuity can make an unending number of equal payments at the end of the interest periods, it is called a perpetuity. If a lump sum investment of $A_n$ is needed to result in n periodic payments of R when the interest rate per period is i, then

$A_n=R\left[\frac{1-{\left(1+i\right)}^{-n}}{i}\right]$

(a) Evaluate $\underset{n\to \infty }{\lim }{A}_n$ to find a formula for the lump sum payment for a perpetuity.

(b) Find the lump sum investment needed to make payments of $100 per month in perpetuity if interest is 12% compounded monthly.