Provide math and assumptions made. Explain reasoning

Retirement Problem.

A client met with a financial consultant to figure out how much she will need to save in order to secure her retirement. There are several scenarios that the financial planner will consider.

a) In exchange of getting paid $30,000 for 8 years starting the beginning of year 6 (i.e., she will get paid $30,000 in the beginning of year 6, 7, and so on for 8 years), she agrees to set aside $x for 5 years, starting now (beginning of year 1, 2, 3, 4, 5). The interest rate is 8%. What is $x?

Draw time-line of all payments she makes and receives.

Clearly write equations for each annuity to be considered. Show all your work.