Today Sarah deposits $$15,000$ into an account that pays $12\%$ per year compounded annually. If after one year, she withdraws $$500.$ After another year, she withdraws another $$500.$ Starting the following year, each withdrawal is $10\%$ more than the previous year $($So$,$ in year $3$ she withdraws $$550).$ If the final withdrawal takes place $7$ years from now. How much will Sarah have left in the account right after her last withdrawal?

$($PLOT the cash flow diagram before solving$)$