Martha is $30$ years old and wants to retire in $20$ years at the age of $50.$ She expects to earn $12\%$ on her savings prior to retirement and $8\%$ thereafter. Martha wants to be able to withdraw $$18,000$ every year at the beginning of each year for $30$ years from the age of $50$ to $80.$ What is the amount that she must deposit at the end of each year for the next $20$ years?