Hello. Answer the following questions clearly explaining your answers.

On 15 May 2007 the government of a country issued an index-linked bond of term 15 years. Coupons are payable half-yearly in arrears, and the annual nominal coupon rate is 4% Interest and capital repayments are indexed by reference to the value of a retail price index with a time lag of 8 months. The retail price index value in September 2006 was 200 and in March 2007 was 206. The issue price of the bond was such that, if the retail price index were to increase continuously at a rate of 7% pa from March 2007, a tax-exempt purchaser of the bond at the issue date would obtain a real yield of 3% pa convertible half-yearly. (i) (a) Derive the formula for the price of the bond at issue to a tax-exempt investor. (b) Show that the issue price of the bond is 61 11.53%. [12] (ii) An investor purchases a bond at the price calculated in (i) and holds it to redemption. The retail price index increases continuously at 5% pa from March 2007. A new tax is introduced such that the investor pays tax at 40% on any real capital gain, where the real capital gain is the difference between the redemption money and the purchase price revalued according to the retail price index to the redemption date. Tax is only due if the real capital gain is positive. Calculate the real annual yield convertible half-yearly actually obtained by the investor. [7] [Total 19]At the end of each year an independent organisation ranks the performance of the unit trusts invested in a particular sector, and classifies them into four quartiles (with quartile 1 being the best performer). Past experience has shown that, at the end of each year, a fund will either remain in the same quartile or will move to a neighbouring quartile. In fact, there is a probability 1-20 that a fund will remain in the same quartile and, where upward or downward movements are both possible, these are equally likely. However, it has been found that a fund that has remained in the top or bottom quartile for two consecutive years has a probability of 1- (#