Hello tutors. Help in solving the following economics questions. Please address them exhaustively.

A life insurance company issues five-year without profit endowment assurances for an annual premium of $3,600 and a sum assured of $20,000 payable on maturity or at the end of the year of death if earlier. The company uses the following assumptions for profit testing: Year Mortality Surrender Expenses at Reserves at Surrender rate rate start year per end of year value at end policy per policy of year per policy 0.01 0.05 (750 E3,100 (2,800 2 0.01 0.05 $15 E6,800 E6.250 3 0.01 0.05 E15 $10,900 $10,000 4 0.01 0.05 E15 (15.300 $14,500 5 0.01 0 $15 Surrenders occur only at the end of a year immediately before a premium is paid. The surrender rates shown in the table above are applied to the number of policies in force at each year-end. (i) Set out the column headings and the formulae you would use to calculate the profit arising each year per policy in force at the beginning of the year. [8] (ii) Calculate (to the nearest 1%) the internal rate of return obtained by the company. Basis: Interest 6% pa [13] [Total 21]A company incurs a liability to pay $1,000(1+0.4r) at the end of year , for / equal to 5, 10, 15, 20 and 25. It values these liabilities assuming that in the future there will be a constant effective interest rate of 7% per annum. An amount equal to the total present value of the liabilities is immediately invested in two stocks: Stock A pays coupons of 5% per annum annually in arrears and is redeemable in 26 years at par. Stock B pays coupons of 4% per annum annually in arrears and is redeemable in 32 years at par. The gross redemption yield on both stocks is the same as that used to value the liabilities. (i) Calculate the present value of the liabilities. [3] (ii) Calculate the discounted mean term of the liabilities. [3] (iii) If the discounted mean term of the assets is the same as the discounted mean term of the liabilities, calculate the nominal amount of each stock which should be purchased. [9] [Total 15]