9. Retirement Planning: Assume that you are 25 and, after spending 3 years after college backpacking across Europe to find yourself, you have just accepted your first job. It pays $60,000 per year and is expected to increase at a rate of 3% per year. You plan to retire at age 65 after working for 40 years. You wish to have enough retirement savings that you can withdraw 90% of your final salary at the end of each of the next 25 years (through age 90).

a) How much must you save at the end of each year during your employment to reach your goal if you can invest in a fund that is expected to pay an 8% return per year compounded annually while you are saving/working, and you continue to earn 8% while you are retired?

b) Assume you have followed the savings plan and have reached retirement age with the total amount you found in part a. By how much would you have to adjust your annual withdrawals during retirement so that your retirement savings still lasts 25 years until you are 90 if returns fall to 4% annually during your retirement (again, returns remain at 8% during your 40 years of employment)?