Riley wants to have $$223,959$ in her savings account in

$9$ years. Riley opened her savings account with an initial

deposit. Riley intends to make equal deposits of $$6,000$

into the savings account at the end of every six months

for the next nine years. Riley will earn $12\%$ interest

compounded semi$-$annually on all deposits with the bank.

Calculate the amount of the initial deposit that Riley

must make in order to have $$223,959$ in her account in

nine years.