This problem shares much with the loan problem discussed recently in class. Suppose you would like to retire with 15 million dollars in savings. To make things simple, let's assume you invest uniform monthly payments for a fixed number of years and that you receive a fixed annual percent yield. Let interest be compounded monthly. Solve this problem using z-transform techniques; I'm not interested in whether you can look up formulas on the internet! Using rates rounded to the nearest (non-zero) half percent (eg., 3 and 4.5 percent are fine, 3.25 percent and 0 percent are not), choose three realistic annual percent yield (interest rates): a low rate isow, an average rate iwe, and a high rate thigh Justify your choices. Next, consider 3 investment time intervals: Dshort 16 years, Dave = 32 years, and Diony = 48 years. The number of retirement payments L is clearly going to be 12 times the duration in years (L = 12D). Let n = 0 correspond to the first investment contribution, let n = 12D - 1 be the last investment contribution, and let n = 12D be the time when the retirement account is to have the desired 15 million dollars in savings. (a) For each interest rate and investment duration, compute the required (fixed) monthly payments Cup needed to realize the 15 million dollar retirement goal. (b) For each interest rate and investment duration, compute the total amount invested (principle). (e) For each interest rate and investment duration, use MATLAB to plot the value of the retirement account as a function of month over the investment interval (it should end at 15 million dollars). On the same graph using a different line style, plot the principle investment as a function of month over the investment interval (it should always be lower than the other curve). Use subplots so that you can print the nine required graphs on a single piece of paper. What do you learn from these computations? Bottom line what seems more important, (realistie) investment duration or (realistic) annual percent yield? What factor do you have most control over? This problem shares much with the loan problem discussed recently in class. Suppose you would like to retire with 15 million dollars in savings. To make things simple, let's assume you invest uniform monthly payments for a fixed number of years and that you receive a fixed annual percent yield. Let interest be compounded monthly. Solve this problem using z-transform techniques; I'm not interested in whether you can look up formulas on the internet! Using rates rounded to the nearest (non-zero) half percent (eg., 3 and 4.5 percent are fine, 3.25 percent and 0 percent are not), choose three realistic annual percent yield (interest rates): a low rate isow, an average rate iwe, and a high rate thigh Justify your choices. Next, consider 3 investment time intervals: Dshort 16 years, Dave = 32 years, and Diony = 48 years. The number of retirement payments L is clearly going to be 12 times the duration in years (L = 12D). Let n = 0 correspond to the first investment contribution, let n = 12D - 1 be the last investment contribution, and let n = 12D be the time when the retirement account is to have the desired 15 million dollars in savings. (a) For each interest rate and investment duration, compute the required (fixed) monthly payments Cup needed to realize the 15 million dollar retirement goal. (b) For each interest rate and investment duration, compute the total amount invested (principle). (e) For each interest rate and investment duration, use MATLAB to plot the value of the retirement account as a function of month over the investment interval (it should end at 15 million dollars). On the same graph using a different line style, plot the principle investment as a function of month over the investment interval (it should always be lower than the other curve). Use subplots so that you can print the nine required graphs on a single piece of paper. What do you learn from these computations? Bottom line what seems more important, (realistie) investment duration or (realistic) annual percent yield? What factor do you have most control over