$3.($a$)$If $30,000$ after$-$tax dollars are invested at $7$ percent in a single$-$premium

tax$-$deferred annuity,how many after$-$tax dollars will be accumulated in

$20$ years?

$($b$)$Studebaker can afford to have his annual income reduced by $3,052$ after$-$

tax dollars.How much is this before taxes?If these before$-$tax dollars are

invested each year at $7$ percent,how many after$-$tax dollars will be accu$-$

mulated in $20$ years?

$($c$)$Redo part$($b$)$assuming $8$ percent is earned during years $1$ to $10,5$ percent

during years $11$ to $15,$and $7$ percent in years $16$ to $20.$