$(10$ points$)$ Find the present value of receiving $$100$ in every period for five periods

when the discount factor, $\backslash$delta is $0\mathrm{.}75.$

ii$)(5$ points$)$ Vin Nguyen won the Powerball lottery in September, $2014.$ Instead

of taking the $$134$M immediate payout, he chose to accept a yearly payment of

approximately $$7\mathrm{.}66$M per year, payments to start immediately and to last for $30$

years. What is the lowest discount factor that makes this decision reasonable for

him?

iii$)(5$ points$)$ What would be the present value of Mr$.$ Nguyen$$s payments if the

payments were for an infinite number of periods, using the discount factor found

in ii$)$ above?