An insurance policy issued to a healthy life provides for death benefits at the end of the year of death of 100 000 if death occurs while healthy or 70 000 if death occurs while unhealthy. In addition there are yearly payments of 30 000 provided the insured is unhealthy. You are given reserves as follows, with state 0 being healthy and state 1 being unhealthy.
5V(0) = 25 000, 5V(1) = 75 000, 6V(0) = 30 000 6V(1) = 60 000
The profit test basis has annual premium of 15,000 paid while healthy, an interest rate of 10%, periodic expenses paid each year of 200 if healthy or 400 if unhealthy, a transition matrix for the year running from time 5 to time 6 and expenses for paying a death claim of 1% of the face amount. Find the profit Pr6 both when the policyholder is healthy at the end of 5 years and when the policy holder is unhealthy at the end of 5 years.