Given a cash flow stream $X=left(x_{0}, x_{1}, x_{2}, ldots, x_{n} ight)$, a new stream $X_{infty}$ of infinite

Given a cash flow stream $X=\left(x_{0}, x_{1}, x_{2}, \ldots, x_{n}\right)$, a new stream $X_{\infty}$ of infinite length is made by successively repeating the corresponding finite stream. The interest rate is $r$. Let $P$ and $A$ be the present value and the annual worth, respectively, of stream $X$. Finally, let $P_{\infty}$ be the present value of stream $X_{\infty}$. Find $A$ in terms of $P_{\infty}$ and conclude that $A$ can be used as well as $P_{\infty}$ for evaluation purposes.