The top prize for the state lottery is $$113,300,000.$ You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option. If you choose the annual payment option and win, you will receive $$113,300,000$ in $16$ equal payments of $$7,081,250-$one payment today and one payment at the end of each of the next $15$ years. If you choose the cash payment, you will receive a one$-$time lump sum payment of $$75,856,113\mathrm{.}14.$ If you can invest the proceeds and earn $7$ percent, which you would choose along with the present value of the annuity? $($Round factor values to $4$ decimal places, e$.$g$.1\mathrm{.}5213$ and final answer to $2$ decimal places, e$.$g$.15\mathrm{.}25.)$