Duration reflects whether the future cash payments of an asset are relatively short-term (low duration) or long-term (high duration). A way to measure duration is given by the following formula: . duration = EF=17 (1 + i)" EF=1 (1 + i)? . where cp, is the cash payment t periods in the future, T is the time to maturity of the asset, and i is the interest rate at which one discounts the future cash payments. Note that following formulas might be helpful aT+1 a1 - a) = -T- (1 - a)2 (1 - a) T=1 and T at a(1 - a") (1 - a) T=1 (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. (5 points) Suppose the price of the consol is $1000. Calculate the duration of a consol that pays $100 each year. Show work. (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. Duration reflects whether the future cash payments of an asset are relatively short-term (low duration) or long-term (high duration). A way to measure duration is given by the following formula: . duration = EF=17 (1 + i)" EF=1 (1 + i)? . where cp, is the cash payment t periods in the future, T is the time to maturity of the asset, and i is the interest rate at which one discounts the future cash payments. Note that following formulas might be helpful aT+1 a1 - a) = -T- (1 - a)2 (1 - a) T=1 and T at a(1 - a") (1 - a) T=1 (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. (5 points) Suppose the price of the consol is $1000. Calculate the duration of a consol that pays $100 each year. Show work. (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