Mr$.$ X has just celebrated his $30$th birthday. He plans to retire on his $65$th birthday.

He has determined that he will need a total of $$400,000$ at that time to fund his retirement.

a$)$ His company offers a $401$k retirement plan that earns $5\%$ compounded monthly.

How much $($rounded to the nearest dollar$)$ should Mr$.$ X deposit at the end of

each month to achieve his retirement goal?

b$)$ Assume that upon reaching age $65,$ Mr$.$ X has attained his goal and has

a total of $$400,000$ in the bank. He now wishes to purchase an annuity that

will make monthly payments for $25$ years $($until he reaches age $90)$; at the end

of that time, the account will be used up$.$

Assuming that he can continue to earn $5\%$ compounded monthly, what

monthly payment will he receive?