a. (5 points) Assume that the interest rate is 5% (i=0.05). Calculate the duration for a zero coupon bond that matures in ten years with a cash payment of $20,000 at the time the bond matures and no cash payments before the maturity date. Show work. b. (5 points) Assume that the interest rate is 10% (i=0.1). Calculate the duration for a bond that pays $1100 in one year, $1210 in two years, and $1331 in three years. What is the present value of this asset today? What is the duration of this asset? 2 C. (5 points) A coupon bond has a face value of $10000 which will be paid at maturity. The coupon bond also has a coupon payment every year of $500 until maturity. The time to maturity is 20 years. What is the duration of that bond? Show work. d. (5 points) Suppose the price of the consol is $1000. Calculate the duration of a consol that pays $100 each year. Show work. e. (5 points) Suppose the current coupon payment is $10. Suppose future coupon payments of the consol are indexed to inflation and inflation is expected to be 2% in the future. The current yield to maturity on the consol is 10%. What is the duration of this consol? Show work