Lucy has been contributing to her daughter, Joan RESP for many years. She contributed a total of $25,000$ and she received a total grant of Canada Education Savings Grant of $$5,000.$ Her first RESP was opened at a bank and at that time she got a Canada Learning Bond of $$400$ as a grant from the Government. Over the years she invested all the money in the account in different securities and the portfolio grew to $$40,000.$ After high school, Joan took a year off to work. However, Joan continued to work for many years afterwards. After $5$ years of working, Joan fell terribly ill and passed away. In the year of Joan$$s passing, Lucy has $$4,000$ in RRSP room and her marginal tax rate is $25\%,$

a$.$ Explain what happens to all the money in the RESP.

b$.$ Calculate the taxes that Lucy has to pay if any, on the accumulated income payments.