Alex is 31 years old and has lived in Los Alamos, New Mexico, for the last four years where he works at the Los Alamos National Laboratory (LANL).LANL provides employees with a 401(k) plan and for every $1 an employee contributes (up to 9 percent of the employee's salary) LANL contributes $3 (a 3 to 1 match).The plan provides a six-year graded vesting schedule. Alex is now in his fifth year working for LANL, and his current year salary is $150,000.Alex's marginal tax rate is 28 percent in 2016.Answer the following questions relating to Alex's retirement savings in 2016.

a. Assume that over the past four years, Alex has contributed $45,000 to his 401(k) and his employer has contributed $115,000 to the plan. The plan has an account balance of $175,000.What is Alex's vested account balance in his 401(k)?

b. Because Alex considers his employer's matching contributions "free money," he wants to maximize the amount of LANL's contributions. What is the least amount Alex can contribute and still maximize LANL's contribution?

c. In need of cash to build a home theater, Alex withdrew $30,000 from his traditional 401(k) account. What amount of the withdrawal, after taxes and penalties, will Alex have available to complete his project?

d. Assume that Alex contributes $10,000 to his traditional 401(k) account this year. Also assume that in 30 years, Alex retires (at age 61) and withdraws the $10,000 contribution made this year and all the earnings generated by the contribution. Also assume that his marginal tax rate at the time he retires is 25 percent. Ignore any prior or subsequent contributions to his plan. If Alex earns a 6 percent annual before-tax rate of return, what are his after-tax proceeds from the distribution?

e. Assume that Alex is 74 years old at the end of the year, retired, and that his marginal tax rate is 25 percent. His account balance in his traditional 401(k) was $1,250,000 at the end of last year. What is the minimum distribution Alex must receive from his 401(k) account for this year? If Alex receives a $43,000 distribution for the year from his 401(k) account (his only distribution during the year) what amount will he be able to keep after taxes and penalties (if any)?