An investment company offers two deals to you. Deal a pays $420$ dollars per year forever. Deal b pays you $80$ dollars every quarter for ten years. You think that both deals are equally risky and your alternative investments provide a return of $12\%$ per year.

a$.$ If deal a will make the first payment five years later, how much are you willing to pay to get deal a$.$

b$.$ If they ask you the price of $1\mathrm{.}583,42$ dollars to get deal b$,$ how much return do you expect to earn from this investment. Which one will you select to invest. Deal a or b$.$ assume that the price of deal a is the same as you calculated in previous question.