Gabriel Martinez estimates that his daughter's college needs, beginning in $9$ years, will be $$3600$ at the end of each quarter for $5$ years. Assume that the investment account earns $6\%$ compounded quarterly.

$1.$ Draw a time diagram for this problem that includes $($i$)$ all payment dates, $($ii$)$ all payment amounts, and $($iii$)$ how the payments are being "moved" throughout time

$2.$ Determine how much money will need to be in the account in $9$ years to fund the annuity $=$ $

$3.$ Determine how much money would need to be invested today so that the correct amount of money will be in the account in $9$ years $=$ $