Sam's Retirement Problem.

1. 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.

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

3. 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).

4. 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.

5. 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.

6. 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.