3. a.Derive an expression for the value and duration of a perpetuity of $c per annum if interest rates are level at r %? The following sums of infinite series might prove useful for your solution: (7 marks)

b.A stock is trading at a price of $50 and has beta 1.5. A call option can be replicated, over a very short period of time, by a portfolio consisting of 0.6 shares of the stock (this is the delta of the call) and a risk-free loan of $20. What is the beta of the call option? (9 marks)

c.The risk-free rate is 3%. The credit-spread of a bond (the difference between the yield-to-maturity and the risk-free rate) is 2%. The face value of the bond is $1,000, and the clean price is $980. The bond has annual coupon payments, and a coupon payment has just been made, with a further 5 coupons remaining. What is the coupon rate of the bond? (9 marks)