Julien has paid $$16,000$ for a retirement annuity from which he will receive $$1,656$ at the end of every three months. The payments are deferred for $11$ years and interest is $11\%$ compounded

quarterly.

$($a$)$ How many payments will Julien receive?

$($b$)$ What is the size of the final payment?

$($c$)$ How much will Julien receive in total?

$($d$)$ How much of what he receives will be interest?