4 a) Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and has a yield to maturity of 6%. Note: The face value of the bond is 1,000. [5 marks] b) What is the duration if the yield to maturity is 10%? Note: The face value of the bond is 1,000. [5 marks] c) An insurance company must make payments to a customer of 10 million in one year and 4 million in five years. The yield curve is flat at 10%. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero- coupon bond, what maturity bond must it purchase? [5 marks]