You have just won a lottery jackpot, and you must choose among the three award options. You can opt to receive a lump sum today of R$61$ million, to receive $10$ end$-$of$-$year payments of R$9\mathrm{.}7$ million, or to receive $25$ end$-$of$-$year payments of R$6$ million. Required: $1\mathrm{.}1.$ If you think he can earn $7\%$ annually, which should he choose? $(4)1\mathrm{.}2.$ If you expect to earn $8\%$ annually, which is the best choice? $(4)1\mathrm{.}3.$ If you expect to earn $10\%$ annually, which option would you recommend? $(4)1\mathrm{.}4.$ Explain how interest rates influence your choice. $($