(6) A 401k is a type of retirement plan offered by many employers. It is very likely that you will eventually have a 401k, (assuming that you dont already). A 401k allows an employee to contribute part of his or her paycheck to a retirement account tax free. Many employers then match a certain percentage of employee contributions to the account.

A 20 year old employee decides to start saving for retirement early. Each month she has $215 deducted from her paycheck into her 401k. In addition to the $215 her employer also matches 65% of contributions employees make to their 401k.

(a) Suppose that the 401k earns 8% interest compounded monthly. How much money will be in the account when the employee retires at age 65? (Hint: First deter- mine the total amount contributed each month to the 401k. Then use the annuity formula).

(b) Suppose that the employee waits until she is 30 to start contributing to her retire- ment account. How much money will be in the account when the employee retires at age 65?

(c) How much money will be in the account at ages 65 if the employee waits until she is 40? What about age 50?