pls write the calculations in each question, thanks (dont use excel nor a financial calculator)

6.42 Assume you will start working as soon as you graduate from college. You plan to start saving for your retirement on your 25th birthday and retire on your 65th birthday. After retirement, you expect to live at least until you are 85. You wish to be able to withdraw $40.000 (in today's dollars) every year from the time of your retirement until you are 85 years old (t.e., for 20 years). The average inflation rate is likely to be 5 percent. a. Calculate the lump sum you need to have accumulated at age 65 to be able to draw the desired income. Assume that the annual return on your investments is likely to be 10 percent. b. What is the dollar amount you need to invest every year, starting at age 26 and ending at age 65 (i.e., for 40 years), to reach the target lump sum at age 65? c. Now answer questions a. and b. assuming the rate of return to be 8 percent per year, then again at 15 percent per year. d. Now assume you start investing for your retirement when you turn 30 years old and analyze the situation under rate of return assumptions of (i) 8 percent, (ii) 10 percent, and (iii) 15 percent. e. Repeat the analysis by assuming that you start investing when you are 35 years old