Exercise 7.5 A special deferred annuity issued to (30) provides the following benefits: A whole life annuity of $10 000 per year, deferred for 30 years, payable monthly in advance. The return of all premiums paid, without interest, at the moment of death, in the event of death within the first 30 years. Premiums are payable continuously for a maximum of 10 years. (a) Write down expressions for (i) the present value random variable for the benefits, and (ii) L0, the future loss random variable for the contract. (b) Write down an expression in terms of annuity and insurance functions for the net annual premium rate, P, for this contract. (c) Write down an expression for L5, the net present value of future loss random variable for a policy in force at duration 5. (d) Write down an expression for 5V, the net premium policy value at time 5 for the contract, in terms of annuity and insurance functions, and the net annual premium rate, P.