Lisa plans to retire on her $61$st birthday. On her $22$nd birthday, Lisa will start saving $A per year for $40$ years. Starting on her $62$nd birthday, Lisa plans on withdrawing $$10,000$ and will continue these annual withdrawals until the account is exhausted on her $85$th birthday. If Lisa$$s bank account pays $3\%$ per year, what annual amount of $A will Lisa need to invest in her bank account to achieve her retirement goal?