Your aunt has just celebrated her 40th birthday. she has two children. one will go to university overseas 10 years from now and requires four beginning-of-year payments for university expenses of $10,000, $11,000, $12,000, and $13,000. the second child will go to another overseas university in 15 years from now and require four beginning-of-year payments for university expenses of $15,000, $16,000, $17,000, and $$18,000. in addition, your aunt plans to retire in 20 years. she wants to be able to withdraw $50,000 per year ( at the end of the year) from an account throughout her retirement. she expects to live 30 years beyond retirement. the first withdrawal will occur on her 61st birthday.

1) what equal, annual, end-of-year amount must your aunt save for each of the next years to meet these goals if all savings earn a 12 percent annual rate of return?

2) what if your aunt expects to receive a lump-sum gift cheque on her 61st birthday for $400,000? show all workings.

3) What are the other actions that your aunt could take to accumulate more savings for her retirement?