1. (a) A bank offers 16% deposit interest rate per annum with continuous compounding, but the interest will be paid quarterly. Determine the interest that should be paid at the end of each quarter for a deposit of $1000. [5 marks] (b) A two-year (i.e. maturity is two years from now) vanilla European call option written on a non-dividend-paying stock is $8 higher than the corresponding put option. The stock price is $3 higher than the strike price of the option. The interest rate is 10% per annum with continuous compounding. Determine the stock price.. [5 marks] (c) The term structure of interest rates (zero curve) is downward sloping. Put the following in order of magnitude and give your reasons a: The 3-year zero rate. 8: The bond-yield of a 3-year bond with semiannual coupon payments. 7: The forward rate of the 3rd year. (5 marks] (d) A product is selling for $1000 now. It has a depreciation rate 10% each year. The annual effective interest rate is 5%. Determine the one-year forward price of the product. [1 marks] (e) Let Pr(t) denote the price at time t of a vanilla European put option on a non- dividend-paying stock. The strike price of the option is K and the maturity is T. The risk-free interest rate is r with continuously compounding. Use no-arbitrate argument to prove Pr(t) < Ke-(-), [6 marks]