Assuming that a disability income insurance policy is issued to Rachel who is (60). The mortality follows the Standard Sickness-Death Model with i = 0.05. The policy pays premiums continuously at a rate of P when the insured is in state 0. The premium is determined using the equivalence principle. The policy pays the following benefits: i. Benefit 1 is a lump sum death benefit at the moment of death of 50,000 ii. Benefit 2 is a disability annuity benefit of 48,000 per year paid continuously while the insured is in state 1. a. Calculate the premium for this policy to the nearest 0.01 . b. Determine 10V(1), the reserve at time 10 for a policy in state 1. c. The insurance company also offers the above benefits in a plan where the premiums are only paid for 10 years. Calculate the premium for this policy. Please note that the benefits do not change. Assuming that a disability income insurance policy is issued to Rachel who is (60). The mortality follows the Standard Sickness-Death Model with i = 0.05. The policy pays premiums continuously at a rate of P when the insured is in state 0. The premium is determined using the equivalence principle. The policy pays the following benefits: i. Benefit 1 is a lump sum death benefit at the moment of death of 50,000 ii. Benefit 2 is a disability annuity benefit of 48,000 per year paid continuously while the insured is in state 1. a. Calculate the premium for this policy to the nearest 0.01 . b. Determine 10V(1), the reserve at time 10 for a policy in state 1. c. The insurance company also offers the above benefits in a plan where the premiums are only paid for 10 years. Calculate the premium for this policy. Please note that the benefits do not change