Future value of an annuity Using the values below, answer the questions that follow. $($Click on the icon here in order to copy the contents of the data table below into a spreadsheet.$)$

$\backslash$table$[[$Amount of annuity,Interest rate,Deposit period $($years$)],[$$$4,000,6\%,12]]$

a$.$ Calculate the future 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 as an investment? Explain why.

a$.(1)$ The future value of the ordinary annuity is $ $($Round to the nearest cent.$)$