24. Rework Example 11.12 if the yield curve is inverted as follows: Term 1 year 2 years 3 years Spot rate 8.75% 8.00% 7.00%

24. Rework Example 11.12 if the yield curve is inverted as follows: Example 11.2 Use formula (11.6) to estimate the price of the bond in Example 11.1 (2) if the yield rate rises to 9%. We first convert the Macaulay duration of 7.2469 (carrying more decimal places) from Example 11.1 (2) to modified duration v=1+id=1.087.2469=6.7101 Per dollar of redemption value, we know that P(.08)=1, since an 8% coupon bond would sell at par. Now applying formula (11.6b), we have P(.09)=P(.08)[1(.01)(6.7101)]=1.067101=.9329. The actual price of the bond is P(.09)=.08a1000+(1.09)10=.08(6.41766)+.422411=.9358 for an error of .9358.9329=.0029, i.e. 29 cents on a $100 bond. Note that if Macaulay duration had been used, rather than modified duration, the answer would have been P(.09)P(.08)[1(.01)(7.2469)]=1.072469=.9275 which has an error of .9358.9275=.0083, i.e. 83 cents on a $100 bond. Clearly, modified duration produces a more accurate answer, as would be expected