Suppose you are now 20 years old and just accepted a new job offer. You would like to save for retirement, but not sure how much you must set aside. You believe that you can earn 4 percent compounded annually on whatever savings you have during retirement years since you would invest conservatively. However, you are confident that before your retirement you would take more risk and could earn 7 percent compounded annually. You plan to retire at the age 62. You believe that your life expectancy is 80 years. You think that that you will need $90,000 per year, starting at the end of the first year in retirement and ending on your 80th birthday. You plan to contribute the same amount at the end of each year while you work. What is the amount of your annual contributions to achieve your retirement income need?

Please show your work!