a) Happy Pet Insurance Company has developed the following life insurance table for cats: Age 5 Age 0 1 2 3 ex 2000 1950 1850 1600 1400 6 7 8 9 lx 1200 1000 700 300 4 0 Happy sells a pet insurance policy on a cat who is age 5. The policy pays a death benefit at the end of the year of death of 1000. Level annual premiums are payable for the life of the cat. The expenses associated with the policy are 10% of premium at the beginning of each year. The interest rate used to calculate all values is 4%. (6 marks) i. Calculate the gross premium for this insurance using Equivalent Principle. (7 marks) ii. Calculate the loss that Happy will incur if the cat dies in the second year if the gross premium is calculated using the Equivalence Principle. (6 marks) iii. Happy decides to charge a gross premium so that the loss will be zero if the cat dies in the second year. Determine the gross premium that Happy decides to charge. a) Happy Pet Insurance Company has developed the following life insurance table for cats: Age 5 Age 0 1 2 3 ex 2000 1950 1850 1600 1400 6 7 8 9 lx 1200 1000 700 300 4 0 Happy sells a pet insurance policy on a cat who is age 5. The policy pays a death benefit at the end of the year of death of 1000. Level annual premiums are payable for the life of the cat. The expenses associated with the policy are 10% of premium at the beginning of each year. The interest rate used to calculate all values is 4%. (6 marks) i. Calculate the gross premium for this insurance using Equivalent Principle. (7 marks) ii. Calculate the loss that Happy will incur if the cat dies in the second year if the gross premium is calculated using the Equivalence Principle. (6 marks) iii. Happy decides to charge a gross premium so that the loss will be zero if the cat dies in the second year. Determine the gross premium that Happy decides to charge