Nicole Clark wants to retire in 15 years. She estimates she will need $43,700 per year during her retirement and she guesses her retirement will last 21 years. She can invest at 5.22% per annum and she pays no tax. Assume all transactions occur at the end of each year so her final payment into the fund is the day before she retires and her first withdrawal is a year after that.

a) How much money must Nicole have accumulated in her retirement fund on the day she retires? 

b) How much money must she save each year to achieve her goal?