Consider the following cases.

Case Annuity payment Interest rate Annuity length $($years$)$

A $$12,0007\%3$

B $55,0001215$

C $700209$

D $140,00057$

E $22,500105$

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$$ordinary or annuity due$$is preferable? Explain why.

Please show your work.