Solve this problem using z-transform techniques; l'm not interested in whether you can look up formulas on the internet! Using rates rounded to the nearest (non-zero) half percent (e.g., 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 ilow, an average rate iave, and a high rate ihigh. Justify your choices. Suppose you decide to invest for retirement over 48 years in the following way: you invest C dollars monthly for the first 10 years, 2C monthly for the next ten years, 3C monthly for the next ten years, and continue this pattern until the last eight years when you are investing 5C dollars monthly. This is somewhat realistic in that most people have more disposable income as they progress in their careers. For each of the three interest rates considered in Problem 1, determine the base payment Ci to achieve a 15 million dollar retirement. How much is invested in principle? What lessons do you learn here