Last week, Bayonetta opened a new wealth management account at the Capital Bank of Noatun to begin

saving for retirement. Today, Bayonetta deposited $$450,000$ into her account. She then plans to make

equal deposits into the account every month for the next $18$ years $($thus$,$ Bayonetta will make a total of

$216$ equal deposits into her account with the first deposit to be made exactly one month from today$).$

Exactly one month after her last deposit is made into the account, Bayonetta wants to withdraw

$$105,000$ per month from the account for a total of $15$ years $($i$.$e$.,$ a total of $180$ withdrawals$).$ If

Bayonetta believes she will earn $12\mathrm{.}5\%$ p$.$a$.$ with monthly compounding on her account over the entire

deposit and withdrawal period, what is the minimum amount that she must deposit every month during

the deposit phase $($i$.$e$.,$ for months $1$ to $216)$ to achieve her withdrawal goal?