I need help for part b. Please show all calculations by hand. Thanks in advance!

On January 1, 2005 Smith deposits 500,000 in an account earning a effective monthly rate of 1%, with interest credited on the last day of each month. Withdrawals are made on the first day of each month starting February 1, 2005, with an initial withdrawal of 1000. Each subsequent withdrawal is 1% larger than the previous one, continuing in this pattern for as long as possible. (a) When does the account finally become exhausted, and what is the amount of the last regular withdrawal? (b) What is the maximum amount the account balance reaches during this process