. After graduating from UTD at age 25, John got his first job at Goldman Sachs with an annual salary of $60,000 a year and a one-time signing bonus of $25,000. He bought a car using his signing bonus. Goldman Sachs offers a 401K retirement investment plan that will match employee's contribution up to 10%. For example if John invests 1% in the 401K account, Goldman Sachs will put in another 1% into his account. John is expecting an annual salary increase of 2.4% (APR on a monthly base. For simplicity, assume that the growth will start in the second month). Suppose, the 401K investment plan will earn him an annual return of 8.4% (APR on a monthly base). (Assume the beginning of age 25 is month 0 and salary is paid at the end of each month, i.e., beginning of age 65 is the last period)

(a) What percentage of salary should John invest in his 401K account in order for him to have $2 million in the account when he retires in 40 years?

(b) At the same contribution rate, if he retires in 35 years instead, how many percent less money will John have?

(c) Instead of buying a nice car, he brought a used car for $10,000, and saved the rest of signing bonus in a separate investment account for retirement that pays 9.6% annual interest (APR on a monthly base). If John wants to have $2 million when he retires in 35 years, what percentage of salary should John invest in his 401K account?