Mr$.x$ has just celebrated his $35$ 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 $5\mathrm{.}75\%$ 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 depleted.

Assuming that he can continue to earn $5\mathrm{.}75\%$ compounded monthly, what monthly

payment will he receive?