Solve this problem using z-transform techniques; I'm not interested in whether you can look up formulas on the internet! 3. Many people contribute to ROTH-variety individual retirement accounts (ROTH IRAs). The max mum allowable ROTH investment is $5,500 annually. Suppose an recent college graduate is considering two options: a) nvesting $5,500 at the beginning of the year from age 22 until age 31 (10 total de- posits) and then ignoring the account until retirement, or b) initially making no investment and then investing S5,500 at the beginning of the year from age 32 until age 64 (33 total deposits). Assuming a historic stock-market average of 7.5 percent APY, which investment option makes most sense? What are the respective account balances when the investor reaches 65 years of age? What is the principle investment in each case? What lessons do you learn here? For those who want to investigate this problem a little more deeply, why might young investors be better served by a ROTH IRA than a traditional IRA? Solve this problem using z-transform techniques; I'm not interested in whether you can look up formulas on the internet! 3. Many people contribute to ROTH-variety individual retirement accounts (ROTH IRAs). The max mum allowable ROTH investment is $5,500 annually. Suppose an recent college graduate is considering two options: a) nvesting $5,500 at the beginning of the year from age 22 until age 31 (10 total de- posits) and then ignoring the account until retirement, or b) initially making no investment and then investing S5,500 at the beginning of the year from age 32 until age 64 (33 total deposits). Assuming a historic stock-market average of 7.5 percent APY, which investment option makes most sense? What are the respective account balances when the investor reaches 65 years of age? What is the principle investment in each case? What lessons do you learn here? For those who want to investigate this problem a little more deeply, why might young investors be better served by a ROTH IRA than a traditional IRA