Question: Answer all the questions below. Please explain your answers fully.

On I January 2008 an investor has a choice of two projects A and B. Project A involves an initial cost of f100,000 and provides income annually in arrear of (5,000 at the end of the first year, inflating at 7% pa, the last payment being on 31 December 2015. The investor will be able to sell the ongoing rights to the project at 31 December 2015 after the payment then due for $130,662. Project B also involves an initial cost of f100,000 and provides no income, but the investor will be able to sell the rights to the project at 31 December 2015 for $197,750. (i) Calculate the internal rates of return for each project as at 1 January 2008, correct to the nearest 0. 1%. [6] (ii) The investor has no capital for investing in either project, but can borrow (100,000 from a bank at 7% pa interest payable annually in arrear. The loan would be repayable on 31 December 2015 at par with no early repayment option. If further loans are required they will also be granted at 7% pa repayable at par on 31 December 2015 with no early repayment option. However, interest on further loans is rolled up to 31 December 2015. If the investor has any surplus proceeds after paying interest on the original loan as it becomes due, these can be invested at an interest rate of 4% pa effective up to 31 December 2015. Calculate the accumulated profit on each project at 31 December 2015. [14] [Total 20]A continuous cashflow is to be paid at a rate p() =10+2t, Ost$10. The force of interest applicable during the period is: 6(1) = 0.05 +0.01, Ost$10 Find the accumulated value of the cashflow at the end of the ten-year period. [6]The mean and standard deviation of the yield, i, on a fund in any year are 0.04 and 0.2 respectively. It is known that 1 + i, is distributed lognormally where i, is the yield in year /. Assuming that yields are independent from year to year, calculate the probability that an investment of (1,000 at time 0 will grow to more than $1,500 at time 5. [8]