A$)$ You have ex actly $35$ years until retirem ent. Your planis to retire with $\backslash (\backslash$$ $5\backslash$mathrm$\{$M$\}\backslash )$ in your retirem ent account ex actly $35$ yearsfrom now. You will be makingm onthly deposits into your relatively risky retirem ent account that is expected to earn either $\backslash (9\mathrm{.}6\backslash \%\backslash$mathrm$\{$APR$\}\backslash )$ or $\backslash (4\mathrm{.}8\backslash \%\backslash$mathrm$\{$APR$\}\backslash )($only ONE of those values can be correct and you have to correctly identify which one$).$ The first deposit equal to $\backslash (\backslash$$ $\backslash$mathrm$\{$X$\}\backslash )$ will be made one month from today, the last deposit will be exactly $35$ years from now $($the day youretire$).$ Every m onth, the am ount of your next deposit will grow by $\backslash (0\mathrm{.}25\backslash \%\backslash )$ compared to the one from the previous month. What will be the value of your first deposit $(\backslash$$X$)?$ B$)$ On the day of your retirem ent $($ex actly $35$ years from today$),$ you will receive the following offer from a financial company: "Give us your $\backslash (\backslash$$ $5\backslash$mathrm$\{$M$\}\backslash )$ today and we will pay you a fix ed am ount of $\backslash (\backslash$$ $270,000\backslash )$ every year for the next $25$ years. The first paym ent will come one year from today, the last paym ent will come $25$ years from today. This is a great deal, because $\backslash (25\backslash$mathrm$\{$x$\}\backslash$$ $270,000=\backslash$$ $6,750,000\backslash ).$ So over the life of the contract, we will pay you $\backslash (\backslash$$ $1\mathrm{.}75\backslash$mathrm$\{$M$\}\backslash )$ more over what you would give us$."$ Whatrate of return will you be earning on this investru ent? $($ii$)$ Given what you know about required rates of return, should you take this offer?