$($b$)$ Your auntie is planning to retire in $6$ years. Currently, she has $$55,000$ in a bond

account and $$82,000$ in a stock account. She plans to add $$9,000$ per year at the end of

each of the next $3$ years to her bond account. The stock account will earn a return of

$8\%$ per year and the bond account will earn a return of $4\%$ per year.

On retirement, your auntie will transfer her money to a savings account which earns an

interest of $2\%$ per year. She hopes to withdraw an equal amount for each of the next $15$

years at the end of each year and have nothing left.

Discuss how you will determine the amount your auntie is able to withdraw each year

during her retirement, and solve for it$.$

$(23$ marks$)$