Mr$.$ Tedd E$.$ Bear wants to start saving for retirement. He estimates that he will withdraw $$144,000$ per year, at the beginning of every year, during retirement. His money will earn $6\%($APR$)$ during this time. Additionally, he expects his retirement to last $30$ years. At the end of his retirement, Mr$.$ Tedd E$.$ Bear would also like to donate $$750,000$ to charity. He currently has $$250,000$ in savings that he will invest in an account that pays $9\%$ APR. If Mr$.$ Tedd E$.$Bear has $18$ years until retirement, what is the yearly investment he needs to make to reach his goal? Assume that the contributions will be made at the end of the year. Additionally, please construct the following:

a$)$ A table that shows the yearly contributions made by Mr$.$ Tedd E$.$ Bear to reach his retirement goal $($i$.$e$.,$ prior to retirement$).$ Hint: The ending balance should equal the amount he needs to save for retirement.

$$ Enter the table in cells M$4$:Q$23.$

$$ The table should span periods $0$ to $18.$

$$ The table must only include relative and absolute references.

$$ The formulas entered in period $1$ should be able to be copied down to the end of the table.

b$)$ A table that shows the year$-$by$-$year balance on the account after retirement. Hint: At the end of the $30$th year, the balance should be equal to zero after the contribution to charity.

$$ Enter the table in cells X$4$:AC$35.$

$$ The table should span periods $0$ to $30.$

$$ The table must only include relative and absolute references.

$$ The formulas entered in period $1$ should be able to be copied down to the end of the table.