A family friend is planning her retirement from work in the U$.$S$.$ She is $62$ years old

right now $($time $0)$ and has the choice of taking her Social Security $($a public pension

program$)$ according to the following schedule $($first payment noted in parentheses$)$:

I. Early retirement at age $62($month $0)$ $$1,400$ per month for life

II$.$ Regular retirement at age $67($month $60)$ $$1,900$ per month for life

III. Delayed retirement at age $70($month $96)$ $$2,400$ per month for life

If her expected life expectancy is $92$ years old $($exactly$),$ what are the present values of

the choices? $($Assume $r=6\%($annually$))$