You are starting your first job as an engineer, and having had a good look at your Engineering Economics course, you decide to plan for your retirement. Assume you are 25 years old (year 0) and plan to work for 40 years, until age 65. After that, you hope to live about 30 years on your pension. Your starting salary will be $76,000 and will increase at a rate of 3% annually by the end of your 40 years of service. In each year of your retirement, you expect to need only 72% of your salary from your last year of employment. The interest rate is 6%. Assume that it will be the same for the next few years and that you invest your savings at this interest rate. a) Calculate the final salary you will earn at age 65 when you retire using (F/P) only. b) How much will you need to have accumulated over the years to provide for your dream retirement at age 65? c) How much will you need to save each year of your career to achieve the amount you found in question 2? d) Rather than investing for all those years, how much would you have to invest today to get the amount you found in question 2? e) Discouraged by all these calculations, you decide to go buy a lottery ticket in the hope of avoiding all the hassles, work, saving for retirement, etc. How much should you win today in the lottery in order to get the same income as you did during your 40-year career