We will do one more quick retirement account analysis problem to see the impact of: (1) trying to save either a fixed amount each year or a constant percentage of your salary each year and (2) starting your retirement saving immediately or waiting 10 years to really start your retirement savings. Lets assume that you put a savings deposit into your 401k account at the end of each year by saving money over that previous year period (i.e. so I normally think of them as beginning of year transactions for my cash flow table since I think of the Period column in my present value table as time elapsed between time zero (e.g. today or whenever the cash flow table starts) and when the cash flow will take place. (e.g. a cash flow in the row labelled Period 1 occurs at the end of Year 0 or beginning of Year 1, so 1 years time has elapsed since time 0) Assume you graduate with your B.S. in Chemical Engineering in Spring semester 2023, take few months off to travel around Europe, and then start work in January 2024 with a starting salary of $70,000. You can also assume where it becomes important that you get an average yearly raise of 2% each year (i.e. so you make $70,000 your first year on the job, $71,400 your second year, etc.). Assume that you are going to retire 40 years later in January 2064. Assume that you are going to live the average of 20 years into retirement, i.e. that you will die in January 2084, and that you want to pay yourself $100,000 per year in retirement income each year, and that both while saving and throughout retirement that your 401k earns 7% in effective interest compounded yearly. Case 1: Using an NPV analysis and assuming that you want to completely expend your retirement savings right when you die (i.e. NPV=0 for the entire series of cash flows then in this case) and that you start saving with your first deposit at the end of 2024, how much would you have to save each year into your retirement account if you wanted to save the exact same amount each year? Case 2: Using an NPV analysis and assuming that you want to completely expend your retirement savings right when you die (i.e. NPV=0 for the entire series of cash flows then in this case) and that you start saving with your first deposit at the end of 2024, how much would you have to save each year on a percentage of your salary basis into your retirement account if you wanted to save the exact same percentage of your salary each year you are working (HINT: Here you may want to add a column to your cash flow table to track your yearly salary as it increase due to raises)? Case 3: Using an NPV analysis and assuming that you want to completely expend your retirement savings right when you die (i.e. NPV=0 for the entire series of cash flows then in this case) and that you have fun in your 20s and early 30s and wait to start saving with your first deposit at the end of 2034 (i.e. so now retirement is only 30 years after you start saving), how much would you have to save each year into your retirement account if you wanted to save the exact same amount each year? Write a short discussion of how you feel about your ability to achieve these types of retirement goals and savings and comment on the effect of waiting to start saving for retirement.