*5.1.9 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 15th year. The company's experience shows that out of 100 new partici- pants, 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 4'h 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 10% through 151" years. The deposits received by the company can be rein- vested at effective annual rate i. (a) Assuming 100 initial participants, find the company's net profit at the end of 15 years, after all plans have been settled, as a function of i, and show that it is an increasing function of i. (b) Wh alue of i gives no net profit to the company? *5.1.9 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 15th year. The company's experience shows that out of 100 new partici- pants, 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 4'h 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 10% through 151" years. The deposits received by the company can be rein- vested at effective annual rate i. (a) Assuming 100 initial participants, find the company's net profit at the end of 15 years, after all plans have been settled, as a function of i, and show that it is an increasing function of i. (b) Wh alue of i gives no net profit to the company