Questions: Refer to the attachments below to answers the questions that follow. Please ensure that you address all questions precisely.

A company incurs a liability to pay $1, 000(1+0.4) 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]Use a general reasoning argument to construct Thiele's differential equation for a regular premium n -year term assurance for a life aged x by considering the change in reserves over a short time period. Assume that: interest is earned continuously at force of interest 8; premiums are payable continuously at rate P - pa; and the sum assured of 1 is payable immediately on death. [5]