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A three-state transition model is shown in the following diagram: Assuming that the transition probabilities are constant at all ages with u = 2%, v = 4%, p = 1%, and a = 5%

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A three-state transition model is shown in the following diagram: Assuming that the transition probabilities are constant at all ages with u = 2%, v = 4%, p = 1%, and a = 5%. Calculate the present value of a sickness benefit of $2000 per year paid continuously to a life now aged 40 exact and sick, during this period of sickness, the force of interest is 4% per annum and the benefit is payable to a maximum age of 60 exact.