I found this document on course hero and I am being ask a similar question for a class, I am just not sure how they arrived at any of the answers. Thank you

Problem 6.37 TVM Comprehensive Assume you will start on a job as soon as you graduate. You plan to start saving for your retirement when you turn 25 years old. (Assume you are 21 years at the time of graduation. Everybody needs a break!) Currently you plan to retire when you turn 65 years old. 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 (i.e., for a period of 20 years). You can invest, starting when you turn 25 years old, in a portfolio fund. 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 your return on the portfolio investment is likely to be 10 percent. Hint: First calculate the inflated value of the yearly retirement income desired for the first year in retirement. Then use the present value of a growing annuity equation to solve for the lump sum required to generate the retirement income stream. Make sure that all cells are properly formatted. Current age: Age when you begin to save for retirement: Age at which you plan to retire: Expected life span: Desired yearly retirement income in today's dollars: Average expected rate of inflation: Desired first year retirement income adjusted for inflation: Return on portfolio investment: 21 25 65 85 $40,000 5.00% $45,681.83 10.00% Amount needed at retirement to fund retirement income: $342,286.01 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? Hint: Solve for the payment in the future value of an annuity equation and then solve using the PMT financial function: PMT(rate,nper,pv,fv,type). Amount needed at retirement to fund retirement income: $281,600.00 Number of years to save for retirement: 40 Annuity payment required (formula): Annuity payment required (function): $636.25 -$636.25 c. Now answer questions one and two assuming your rate of return to be 8 percent per year, and then 15 percent per year. Return on portfolio investment: 8.00% Amount needed at retirement to fund retirement income: $342,286.01 Number of years to save for retirement: Annuity payment required (formula): Annuity payment required (function): Return on portfolio investment: 40 $19,919.46 15.00% Amount needed at retirement to fund retirement income: $342,286.01 Number of years to save for retirement: Annuity payment required (formula): Annuity payment required (function): 40 $1,692.64 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. Return on portfolio investment: 8.00% Amount needed at retirement to fund retirement income: $5,160,266.49 Number of years to save for retirement: Annuity payment required (formula): Annuity payment required (function): Return on portfolio investment: 35 $29,946.39 10.00% Amount needed at retirement to fund retirement income: $4,353,086.79 Number of years to save for retirement: Annuity payment required (formula): Annuity payment required (function): 35 $16,061.61 Return on portfolio investment: 15.00% Amount needed at retirement to fund retirement income: $3,011,353.29 Number of years to save for retirement: Annuity payment required (formula): Annuity payment required (function): 35 $3,417.45 e. Repeat the analysis by assuming that you start investing only when you are 35 years old. Return on portfolio investment: 8.00% Amount needed at retirement to fund retirement income: $5,160,266.49 Number of years to save for retirement: Annuity payment required (formula): Annuity payment required (function): Return on portfolio investment: 30 $45,551.91 10.00% Amount needed at retirement to fund retirement income: $4,353,086.79 Number of years to save for retirement: Annuity payment required (formula): Annuity payment required (function): Return on portfolio investment: 30 $26,463.49 15.00% Amount needed at retirement to fund retirement income: $3,011,353.29 Number of years to save for retirement: Annuity payment required (formula): Annuity payment required (function): 30 $6,926.71 ent when you turn 25 ntly you plan to retire sh to be able to withdraw d (i.e., for a period of 20 ation rate is likely to be 5 desired income. Assume n retirement. Then use the etirement income stream. t age 65 (i.e., for 40 MT financial function: r, and then 15 percent alyze the situation under 35 years old