6. (20 points) Applications of discr You graduate UMKC and start working for an employer that provides a 50% match to the amount you invest each month toward your retirement. This means for every $1 you invest, your employer adds $0.50 at the same time. You plan to obtain an 8% yearly investment interest rate. You start with $o in your account. You plan to invest for 40 years. How much would you have at retirement if you put in $10,000 per year? This means $15,000 total is put into the account per year. (a)(s points) Show the setup of the problem and how the numbers above would be used in the problem (b) (10 points) Solve for the total amount at retirement using z-Transforms. (e) (s points) What percentage of the final amount in part(b) is interest? If you were not able to find a value in part (b), use an answer to part (b) of $2 million 9