Consider a permanent disability model with three states: state 0 is healthy; state 1 is disabled; and state 2 is dead. Transition intensities are constant. =0.04, =0.02, and =0.07. Assume a force of interest =10%.

An insurance policy issued to age (x), healthy at the time of issuance, provides the following benefit:

(i). A continuous annuity of payment rate of 600 per annum is payable for at most 3 months starting at the time when insured becomes disabled.

(ii). A lump sum benifit of 50 is payable 3 months after the insured become disabled, if the insured is still alive.

(iii). A death benefit of 3000 is payable at the moment of death, if death occurs within the 3 months period after the insured becomes disabled.

(iv). Payment ceases 3 months after the insured becomes disabled.

#Calculate the actuarial present value of the (a)continuous annuity, (b)lump and (c)the death benifit of 3000.

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