**Solve using Excel**

1) Perpetuity Duration: A perpetuity promises a stream of regularly occurring cash flows for an infinite amount of time. The par (or face value) of the bond is never returned to the investor. Suppose the par value is $100 and the perpetuity promises a 4% annual coupon. The yield of the bond is 3%, expressed in continuously compounded terms. You can't model cash flows to infinity in Excel, but you can approximate the duration and convexity of a perpetuity by using a long term. a) Calculate the price, duration and convexity of the perpetuity assuming the cash flows only last for 500 years. Write your answers using 2 decimal points. (8 points) Assume now that the yield changes to 3.1%: b) Calculate the approximate percent price change using duration only. Write your answer using 4 decimal points. (3 points) c) Calculate the approximate percent price change using duration and convexity. Write your answer using 4 decimal points. (3 points) d) Calculate the actual percent price change by recalculating the price of the perpetuity at a 3.1% yield. Write your answer using 4 decimal points. (3 points) 1) Perpetuity Duration: A perpetuity promises a stream of regularly occurring cash flows for an infinite amount of time. The par (or face value) of the bond is never returned to the investor. Suppose the par value is $100 and the perpetuity promises a 4% annual coupon. The yield of the bond is 3%, expressed in continuously compounded terms. You can't model cash flows to infinity in Excel, but you can approximate the duration and convexity of a perpetuity by using a long term. a) Calculate the price, duration and convexity of the perpetuity assuming the cash flows only last for 500 years. Write your answers using 2 decimal points. (8 points) Assume now that the yield changes to 3.1%: b) Calculate the approximate percent price change using duration only. Write your answer using 4 decimal points. (3 points) c) Calculate the approximate percent price change using duration and convexity. Write your answer using 4 decimal points. (3 points) d) Calculate the actual percent price change by recalculating the price of the perpetuity at a 3.1% yield. Write your answer using 4 decimal points. (3 points)