Rupert is planning to retire from his job later this month at age 65. He expects to withdraw a constant amount of money from his savings account every month throughout his retirement years. The total amount of his savings is $500,000.

a. How much money can Rupert withdraw from his savings account at the end of every month until the balance in his account declines to zero at age 86. Assume he earns a 4% APR compounded monthly on his savings account throughout his retirement years.

b. Assume Rupert withdraws $15,000 from his savings account on the occasion of his 70th birthday to cover the cost of a family reunion, calculate his account balance at age 70th. You are to assume he continues to withdraw the same amount of money from his savings account every month calculated in part (a) above and he earns 4% APR compounded monthly on his savings.