Inaaya is a diligent mother who has just finished supporting her two children, Michael, aged $23,$ and Emily, aged $25,$ through their university education. Both Michael and Emily have embarked on their careers and have moved out. Inaaya wants to continue supporting them by providing financial assistance for their future endeavors, such as purchasing their first home or pursuing further education. She aims to give each of them an equal amount of money when they reach the age of $30.$ Currently, Inaaya has $$15,000$ in savings, which she plans to allocate to Emily, as she will reach $30$ first. She intends to provide Emily with $$35,000.$ Inaaya's investments generate a $6\%$ return before tax, and her marginal tax rate is $35\%.$ The inflation rate is estimated to be $3\%.$

All savings are deposited at the end of the year.

Required:

$1.$ Calculate the annual savings Inaaya needs to make in order to accumulate $$35,000$ to give to Emily when she turns $30.$

$2.$ Determine the fair amount Inaaya should give to Michael when he reaches $30,$ considering that Emily will receive $$35,000.$

$3.$ Compute the annual savings Inaaya should make, starting now, to reach the amount calculated in $($b$)$ for Michael.

$4.$ Inaaya's mortgage will be paid off in three years. Until then, she can only contribute a total of $$3,500$ per year to the "children's fund". After the mortgage is paid off, Inaaya can allocate up to $$25,000$ per year. Calculate the annual savings Inaaya needs to make after the mortgage is repaid to achieve her goal for Michael.

$5.$Would the income attribution rule apply in this case? Why or why not?