A $22$ years old new hire $($at t$=0)$ is planning for retirement at age $65($at t$=43).$ The new employee plans to save $$2,000$ per year for the next $15$ years $($t$=1$ to t$=15).$ The savings are estimated to earn $8\%$ per year on average. At $65,$ the person wants to have a retirement income of $$90,000$ per year or $20$ years, with the first withdrawal occurring at t$=43$ right after last saving payment is deposited.

How much money must be saved each year from t$=16$ to t$=43$ to attain the desired retirement goal.