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

$\backslash$table$[[$Case$,$Annuity payment,Interest rate,Annuity length $($years$)],[$A$,$$$12,000,7\%,3],[$B$,55,000,12,15],[$C$,700,20,9],[$D$,140,000,5,7],[$E$,22,500,10,5]]$

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 annuityordinary or annuity due$-$is preferable? Explain why.