You just turned $21$ years old and want to retire when you turn $65.$ You expect to live for $25$ years after retirement and want to withdraw $$50,000$ per year in retirement, starting on your $65$th birthday.

You expect to earn a return of $7\%$ on your investments every year. What is the total present value $($as of your $65$th birthday$)$ of the withdrawals you expect to make in retirement? You want to save a constant amount every year. How much money should you save each year if you make the first deposit now and the last one one year before you turn $65?$