You are planning for retirement. First, you would like to be able to retire $30$ years from now with a retirement income stream of $$100,000$ per year for $20$ years, wich the first perment received $31$ years from now $($exacty$,$ one year after your retitement$),$ Second, you would like to leave an inheritance of $$1\mathrm{.}000,000$ to your children at your death, which we will assume takes place at the end of $20$ years of withdrawals. To meet these goals, you will deposit some of your income inso a savings account each year until retirement. You plan on growing the amount you deposit at a constant rate of $1\%$ per year until retirement. Your first deposit will be at the end of this year. Assume that the EAR of $7\%$ and that you do not have any starting savings. $1$ A$.$ Compute the amount that you will require in your account at your retirement date $($end of year $30)$ to meet your retirement goals. B$.)$ Determine how much money you must deposit at the end of the first year $($as part of your

planned $30$ contributions until retirement$)$ to exactlv meet vour retirement goals C$.)$ Now suppose that you will receive a one$-$time inheritance of $$200,000$ ten years from

now $($at the end of year $10).$ Given this additional money in your savings account, how

much could vou spend each ver in retirement? Assume the other parameters of the

problem $($retirement age, savings plan, end date, inheritance$)$ remain the same as in parts

AandB.