Today, you celebrated your 30th birthday. You just landed a new job at Citi Bank. Citi provides you a 401-k plan, and you decide to deposit $250 every month for 15 years. City matches your 401-k at 100. However, the matched deposit of 12(250) = $3,000 are made once a year, at the end of the year. Citi pays interest at6% compounded monthly. At the end of 15 years you change the job to JP Morgan Chase, and you decide to roll-over your entire 401-k to Chase. At Chase, you contribute 6% of your salary to the 401-k; deposits are made annually. Your starting salary at Chase is $80,000 and you expect to earn 3% pay raise every year. Chase matches your 401-k at 66.6667% (matching funds are deposited annually), and pays interest at 7% per year. You retire from Chase when you reach 65. You had a hardship withdrawal of $30,000 at age 55. The money was returned to account at age 60. On your 65th birthday, and you stop contributing to 401-k. 

a) Determine the total account balance (including company match) in your Chase account on your 65th birthday. 

b) After you reach age 70, you start withdrawing $6,000 every month until death. Also, you withdrew $30,000 (a one-time withdrawal for the birthday party) on your 75th birthday. Determine the balance in the account on your 90th birthday.