An investment company offers a 15-year double your money savings plan, which requires a deposit of 10,000 at the start of each year for 15 years. At the end of 15 years each participant receives 300,000. If a participant opts out of the plan, he gets back his deposits accumulated at 4% up to the time he opts out. Opting out occurs at the start of a year when a new payment is due, from the start of the 2nd to the start of the 5th year. The companys experience shows that out of 100 new participants, the numbers that opt out each year are 5 at the start of the 2nd year, 4 at the start of each of the 3rd and 4th years, 3 at the start of each of the 5th and 6th years, 2 at the start of each of the 7th through 9th years, and 1 at the start of each of the 10th through 15th years. The deposits received by the company can be reinvested at effective annual rate z. (a) Assuming 100 initial participants, find the companys net profit at the end of 15 years, after all plans have been settled, as a function of z, and show that it is an increasing function of z. (b) What value of z gives no net profit to the company?