$($a$)$ You belong to an unusual pension plan because your retirement payments will

continue forever $($and will go to your descendants after you die$).$ If you will receive

$$48,000$ per year at the end of each year starting $40$ years from now $($i$.$e$.,$ the first

payment is in time $40),$ what is the present value of your retirement plan if the discount

rate is $6\%?$

$($b$)$ How does your answer to part $($a$)$ change if you will receive $$4,000$ per month every

month forever $($in perpetuity$)$ starting $40$ years from today $($the first payment is in time

period $480)$ and you compound monthly?