Actuarial CM1

a Investor A purchases 1,000 nominal of a 4-year bond which pays coupons annually in arrears at the rate of 6% p.a. and is redeemed at par. After 2.25 years Investor A sells a proportion r of her holding of the bond to Investor B; after a further six months Investor A sells a proportion r2 of her initial holding of the bond to Investor C; and after a further six months Investor A sells her remaining holding of the bond to Investor D. Investors B, C and D each keep their holdings of the bond until its maturity. Suppose that the price paid by Investors B and C to Investor A for their holdings of the bond is the same and that the price paid by Investor D to Investor A for his holding of the bond is 200. Suppose that Investors B, C and D each obtain an annual gross yield of 6% p.a. on their respective bond transactions'. (a) Calculate the price paid by Investor B to Investor A for his holding of the bond. [5] (b) Calculate the initial price paid by Investor A for her holding of the bond if she made an annual gross yield of 5% p.a. on her entire subsequent bond transactions. [2] Suppose that Investor A pays income tax at the rate of 20% and capital gains tax at the rate of 30%. (c) Use 2 iterations of linear interpolation to estimate the annual net yield made by Investor A on her entire bond transactions. [3] a Investor A purchases 1,000 nominal of a 4-year bond which pays coupons annually in arrears at the rate of 6% p.a. and is redeemed at par. After 2.25 years Investor A sells a proportion r of her holding of the bond to Investor B; after a further six months Investor A sells a proportion r2 of her initial holding of the bond to Investor C; and after a further six months Investor A sells her remaining holding of the bond to Investor D. Investors B, C and D each keep their holdings of the bond until its maturity. Suppose that the price paid by Investors B and C to Investor A for their holdings of the bond is the same and that the price paid by Investor D to Investor A for his holding of the bond is 200. Suppose that Investors B, C and D each obtain an annual gross yield of 6% p.a. on their respective bond transactions'. (a) Calculate the price paid by Investor B to Investor A for his holding of the bond. [5] (b) Calculate the initial price paid by Investor A for her holding of the bond if she made an annual gross yield of 5% p.a. on her entire subsequent bond transactions. [2] Suppose that Investor A pays income tax at the rate of 20% and capital gains tax at the rate of 30%. (c) Use 2 iterations of linear interpolation to estimate the annual net yield made by Investor A on her entire bond transactions. [3]