A 10-year maturity zero-coupon bond selling at a yield to maturity of 7.25% (effective annual yield) has convexity of 157.5 and modified duration of 9.06 years. A 30-year maturity 7.5% coupon bond making annual coupon payments also selling at a yield to maturity of 7.25% has nearly identical duration—9.04 years—but considerably higher convexity of 251.6.

Now ray has had the tires for two months and he notices that the tread has started to pull away from the tire. he has already contacted the place who sold the tires and calmly and accurately explained the problem. they didn’t him because they no longer carry that tire. so he talked with the manager and he still did not get the tire replaced. his consumer rights are being violated. pretend you are ray and write a letter to the company’s headquarters. here are some points to keep in mind when writing the letter: include your name, address, and account number, if appropriate. describe your purchase (name of product, serial numbers, date and location of purchase). state the problem and give the history of how you tried to resolve the problem. ask for a specific action. include how you can be reached.