Project on Simpson's Numerical Method using R 02 02 Consider a permanent disability model with three states: State 0: Healthy, State 1: Permanently disabled, and State 2: Dead. Suppose that = A+ Bear, 12 = Cebu, 2 = 92 for x > 0 An insurance company uses the model to calculate premiums for a 20-year term insurance policy issued to a life aged 30 who is now healthy. The death benefit is S, payable at the moment of death. Premiums are payable monthly in advance provided that the policyholder is healthy. Use Simpson's Numerical Method with 100 subintervals to 1. Calculate the monthly premium for this policy on the following basis: Interest: constant force of interest of 6% per year Initial expense: 60% of the gross premium Renewal expenses: 10% of each of the premium except the first. 2. Calculate the gross premium reserve at times 5, 10 and 15 for a policyholder who is healthy by that times. 3. Calculate the gross premium reserve at time 5, 10 and 15 for a policyholder who is permanently disabled by that times. A B C a T 0.000033 0.000038 0.000053 0.23 0.21 230000 Project on Simpson's Numerical Method using R 02 02 Consider a permanent disability model with three states: State 0: Healthy, State 1: Permanently disabled, and State 2: Dead. Suppose that = A+ Bear, 12 = Cebu, 2 = 92 for x > 0 An insurance company uses the model to calculate premiums for a 20-year term insurance policy issued to a life aged 30 who is now healthy. The death benefit is S, payable at the moment of death. Premiums are payable monthly in advance provided that the policyholder is healthy. Use Simpson's Numerical Method with 100 subintervals to 1. Calculate the monthly premium for this policy on the following basis: Interest: constant force of interest of 6% per year Initial expense: 60% of the gross premium Renewal expenses: 10% of each of the premium except the first. 2. Calculate the gross premium reserve at times 5, 10 and 15 for a policyholder who is healthy by that times. 3. Calculate the gross premium reserve at time 5, 10 and 15 for a policyholder who is permanently disabled by that times. A B C a T 0.000033 0.000038 0.000053 0.23 0.21 230000