Emma from Rosehaven Vets is putting together a one-year pet insurance policy, covering death and dread disease for quokkas. Emma’s research has

found that

• the probability that a healthy quokka of insurable age survives one year is 0.9,

• the probability that such an animal develops depression in a one-year period is 0.1 and

• the probability that a healthy quokka of insurable ages develops muscular dystrophy in a one-year period is 0.05.

Rosehaven Vets insurance policy will pay benefits (one year from the policy issue date) if an insured quokka either dies or develops depression or muscular

dystrophy (or both) during the policy year. The benefit schedule is as follows:

• $2 500 is paid at year end if the quokka develops muscular dystrophy,

• $5 000 is paid at year end if the quokka develops depression,

• $7 500 is paid at year end if the quokka develops both muscular dystrophy and depression, or

• $10 000 is paid on death.

Rosehaven Vets incurs an initial expense of $50 per policy when it is issued. There are further costs of $150 at year-end if a claim is paid. Further, Rosehaven Vets wants the policy to generate a profit of 5% of premiums. Emma has determined the appropriate interest rate to use for pricing is 6% p.a.

a. Emma has calculated that the probability of a healthy quokka surviving one year and being disease-free is 0.769 5, the probability of a

healthy quokka surviving one year and developing depression is 0.085 5, the probability of a healthy quokka surviving one year and developing muscular dystrophy is 0.040 5 and the probability of a healthy quokka surviving one year and developing both depression and muscular dystrophy is 0.004 5. Explain how Emma arrived at these four numbers.

b. Draw a detailed contingent cash flow diagram that models this pet insurance policy from the perspective of Rosehaven Vets

c. What is the premium Rosehaven Vets will charge for this pet insurance policy?