the top prize for the state lottery is $108,500,000.$ You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option$/$ If you choose the annual payments option and win, you will receive $108,500,000$ in $25$ equal payments of $4340000-$ one payment today and one payment at the end of the next $24$ years. if you choose the cash payment, you will receive a one$-$time lump sum payment of $58808551\mathrm{.}67.$ you can invest the proceeds and earn $7\%.$ At what interest rate would you be indifferent between the cash and annual payments option?