David bought a unique 20-year insurance-cum-savings plan which allows him to choose one of the following two options: 

Option 1: Contribute a fixed sum at the end of every month. 

Option 2: Contribute a fixed sum at the end of each of the first ten months (January to October) of every year, with no contributions required for the months of November and December. This special option is structured to meet the needs of individuals who may have high year-end expenses. The annual nominal interest rate earned in the plan is 6%, with interest compounded monthly. 

(a) What amount of monthly contribution must David make in order to have $500,000 at the end of 20 years if he chooses Option 1? 

(b) If David chooses Option 2, and still wants to have $500,000 at the end of 20 years, what amount of monthly contribution must he make in the first ten months of each year?