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.



b) Solve for $x except that now interest rate is 5%. All other assumptions are as in a).



c) Solve for $x except that now she would like to have a more expensive lifestyle in retirement and will need $40,000 withdrawal each year (instead of $30,000). All other assumptions are as in a).



d) Assume interest rate is 8%, and everything else is as in a) except that the client actually has some savings to contribute to the retirement. Specifically, she will allocate $50,000 to retirement in the beginning of year 1 (In the retirement problem, account balance beginning of year 1 is $50,000). Solve for $x.



e) Now, assume that everything is the same as in a) except that all payments are made at the end of each year (and not beginning of each year as above), calculate $x.



f) Now, assume that a client actually will live forever, and would like to receive $30,000 each year starting in year 6 forever. Assume that all payments are made at the end of each year. Clearly show new equations you are going to use. Solver for $x.