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 also enjoys an annual salary increase of 2.4% (APR on a monthly base) starting in the second month. Suppose, the 401K investment plan will earn him an annual return of 8.4% (APR on a monthly base). (Assume that 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. )

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

John will transfer her money at the age of 65 (his retirement) from his 401K account (valued at $2 million) into a safe account which will earn an annual interest of 3.6% (APR on a monthly base).

(c) If he wants to use up all his money at the age of 90, how much can he spend each month after

retirement?

(d)With the increase in life expectancy, John does not know how long he will live. So he buys a whole life annuity using all of his money at retirement. Assuming the same 3.6% return, how much would the annuity pay him each month? (hint: the whole life annuity is just like a perpetuity)

(e)If John actually dies at the age of 90, how much he could pass to his children if he does not buy the whole life annuity but consumes $7000 a month?