Answer the following questions

A life company sells 25-year with-profit endowment assurances to lives aged 30 exact. The basic sum assured is $50,000, and compound bonuses of 1.923% are added to the sum assured at the end of each year. The death benefit is payable at the end of the year of death, after the bonus amount for the current year has been added. Level premiums are payable monthly. The basis is as follows: Mortality: AM92 Select Interest: 6% pa Expenses: Initial, 30% of the first year's premiums, payable at the start of the contract Renewal, 5% of all premiums, including the first year, payable at the start of each year. (1) Show that the monthly premium is $130.91. [6] (ii) Find the gross premium prospective reserve just before the start of the tenth year of the policy, assuming that bonuses have been declared according to the initial assumptions. [6] [Total 12]A 10-year temporary annuity is payable continuously to a life now aged x. The rate of payment is 100 pa for the first 5 years and 150 pa for the next 5 years. (i) Write down an expression in terms of 7, for the present value of this annuity. [3] (ii) Calculate the expected present value of the annuity assuming a constant force of interest of 0.04 pa and a constant force of mortality of 0.01 pa. [8] [Total 11]