P$5-22$ Present value of an annuity Consider the following cases.

$\backslash$table$[[,,,],[$Case$,$Annuity payment,Interest rate,Annuity length $($years$)],[$A$,30,000,8\%,3],[$B$,24,000,12,15],[$C$,8,000,5,20],[$D$,160,000,9,8],[$E$,72,000,10,12]]$

a$.$ Calculate the present value of the annuity, assuming that it is

$(1)$ An ordinary annuity.

$(2)$ An annuity due.

b$.$ Compare your findings in parts $a(1)$ and $a(2).$ All else being identical, which type of annuity is preferable$-$ordinary or annuity due? Explain why?