Question 1 (25 marks) [Each part is independent.] a) You have won a lottery and can choose to receive the payment under one of the following two arrangements: (1) $250,000 every six months forever, or (2) fixed payments of $X every six months for 15 years. Suppose the relevant half-yearly rate is 5% and the payments under both arrangements will start immediately. i) How much is the lottery worth today under Arrangement (1)? (4 marks) ii) What is the amount of $X in Arrangement (2) so that it has the same value as Arrangement (1)? (4 marks) b) Calculate the total amount of interest on interest earned five years from now if $100,000 is deposited into a bank account today that earns 5% interest per year. (4 marks) c) ABC Corporation issued at par $ 100 million semi-annual coupon-paying bonds on January 1, 2010. The bond's YTM at issuance was 8% (APR). The bond matures on January 1, 2020. i) Compute the market value of this bond on January 1, 2011 if it was priced to produce an effective semi-annual yield to maturity of 6% on that date. (5 marks) ii) Assume the bond is sold on January 1, 2011. Calculate the current yield and 1- year capital gains yield (CGY 1-year). (6 marks) iii) Can the 1-year total yield be determined by the sum of current yield and capital gains yield? Explain your answer. (2 marks)