Refer to the attachment. Clear explanations.

6 A 17-year with-profits endowment assurance is issued to a life aged exactly 48, having a basic guaranteed sum assured of 25,000. The sum assured plus all declared reversionary bonuses to date are paid on survival to the end of the term or immediately on earlier death. Calculate the expected present value of this policy benefit assuming: future bonuses are declared at the rate of 2.5% pa compound, being added in full at the start of each policy year AM92 Select mortality 6.6% po interest. 7 A woman aged 67 exact takes out an annuity that makes monthly payments in arrears. The first tyle monthly payment is f1,500, and payments increase by 0.23726% each month. Calculate the expected present value of the annuity using the following basis: Mortality: PFA92C20 Interest: 7% per annum (4] 8 A whole life assurance policy pays 20,000 on death in Year 1, 20,100 on death in Year 2, and so on lyle increasing by 100 each year. The payment is made immediately on death of a life currently aged 35 exact. (1) Write down an expression for the present value random variable of this payment, in terms of the curtate future lifetime Ky , and/or the complete future lifetime Tx . [1] (ii) Calculate the expected present value of these benefits, assuming: (a) AM92 Select mortality and 6% po interest (b) a constant force of mortality of 0.015 pa and force of interest 0.03 pa. (11) [Total 12] 9 A whole life annuity with continuous payments is due to commence in 15 years' time. It will be tyle payable to a life that is currently aged exactly 50, provided that person is still alive when the annuity is due to start. Payments commence at the rate of 20,000 pa, and increase continuously thereafter at a rate of 2% pa compound. Calculate the expected present value of these payments on the following basis: Mortality: PMA92C20 prior to age 65 A constant force of 0.038 po at ages over 65 Interest: 3% pa effective [6]A life insurance company issues whole life assurance policies to lives aged 50 exact for a sum assured of f75,000 payable at the end of the year of death. Premiums are payable annually in advance. (i) Calculate the annual gross premium for each policy using the basis below. [4] (wi) Calculate the minimum annual gross premium that the company should charge in order that the probability of making a loss on any one policy would be 10% or less. [6] Basis: Mortality: AM92 Select Interest: 6% per annum Initial commission: 100% of the annual gross premium Initial expenses: 6325 Renewal commission: 2.5% of each annual gross premium excluding the first Renewal expenses: 675 per annum at the start of the second and subsequent policy years [Total 10] A life aged 60 exact purchases a special deferred term assurance policy for an overall term of 20 years. Under this policy a sum assured of $100,000 is paid on death but only on death from age 65 exact up to the end of the term. On death between age 60 and 65 the benefit is equal to the total premiums paid without interest. All payments on death are made at the end of the year of death. An annual premium paid in advance is payable for the full 20 year term. Calculate the annual premium payable. [7] Basis: Mortality AM92 Ultimate Interest 4% per annum Expenses Ignore