The annuity framework provides an alternative method to expressing a net present value$($NPV$)$ analysis.$$This annual worth method has the advantage that it expresses its results in terms of a constant$$level of cash flow and thus is easily understood. Suppose a project has an associated cash flow stream$($x$0,$ x$1,...,$ xn$)$ over n years. A present value analysis uses a $($fictitious$)$ constant ideal bank with interest$$rate r to transform this stream hypothetically into an equivalent one of the form $($V$,0,0,...,0),$where V is the net present value of the stream. An annual worth analysis uses the same ideal bank$$to hypothetically transform the sequence to one of the form $(0,$ A$,$ A$,$ A$,...,$A$).$ The value A is the$$annual worth $($over n years$)$ of the project. It is the equivalent net amount that is generated by the$$project if all amounts are converted to a fixed n$$year annuity starting the first year.$1.$ Given a cash flow stream X $=($x$0,$ x$1,...,$ xn$),$ a new stream X$\backslash$infty of infinite length is made by$$successively repeating the corresponding finite stream. The interest rate is r$.$ Let P and A be$$the present value and the annual worth, respectively of stream X$.$ Finally, let P$\backslash$infty be the present$$value of stream X$\backslash$infty $.$ Find A in terms of P$\backslash$infty and conclude that A can be used as well as P$\backslash$infty for$$evaluation purposes.