Discuss your observation on the attached duration approximation.
4.5 0.5 1.625 1.616935434 Bond price change: Yield 1.0-1.5% T Ct PV (Ct) & 1.000% PV(Ct)*t PV (Ct) & 1.500% Duration (annual compunding) Modified duration Approx. change in bond price Actual bond price change 1 1.5 2 2.5 3 3.5 4 5 5.5 6 6.5 7 7.5 8 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 101.625 1.608910891 1.600926171.59298108 1.58507542 1.57720899 1.5693816 1.56159306 1.55384317] 1.54613174 1.53845858 1.53082351 1.52322632 1.51566684 1.50814487 93.8489825 117.27829 1.608910891 2.40138926 3.18596216 3.96268855 4.73162697 5.49283561 6.24637224 6.99229427] 7.73065871 8.46152222 9.18494104 9.90097109 10.6096679 11.3110865 750.79186843.421255 1.600985222 1.58911125 1.57732534 1.56562685 1.55401511 1.5424895 1.53104937 1.51969409 1.50842303 1.49723556 1.48613106 1.47510893 1.46416853 1.45330929 90.213643 113.191264 0.808467717 1.612947918 7.192 7.120418863 -$4.1754 -$4.0870 Bond price change: Yield 1.0-2.0% T Ct 0.5 1.625 1.616935434 0.808467717 1.608989757 7.192 7.120418863 -$8.3507 -$8.0030 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 101.625 1.608910891 1.60092617| 1.59298108 1.58507542 1.57720899 1.5693816 1.56159306 1.55384317| 1.54613174 1.53845858 1.53082351 1.52322632 1.51566684 1.50814487 93.8489825 117.27829 1.608910891 2.40138926 3.18596216 3.96268855 4.73162697 5.492835616.24637224 6.99229427| 7.73065871 8.46152222 9.18494104 9.90097109 10.6096679 11.3110865 750.79186843.421255 1.593137255 1.57744094 1.56189927 1.54651072 1.53127379 1.51618698 1.50124882 1.48645783 1.47181257 1.4573116 1.4429535| 1.42873686 1.41466029 1.40072241 86.735959 109.275302 PV (Ct) &1.000% PV(Ct)*t PV (Ct) &2.000% Duration (annual compunding) Modified duration Approx. change in bond price Actual bond price change 4.5 0.5 1.625 1.616935434 Bond price change: Yield 1.0-1.5% T Ct PV (Ct) & 1.000% PV(Ct)*t PV (Ct) & 1.500% Duration (annual compunding) Modified duration Approx. change in bond price Actual bond price change 1 1.5 2 2.5 3 3.5 4 5 5.5 6 6.5 7 7.5 8 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 101.625 1.608910891 1.600926171.59298108 1.58507542 1.57720899 1.5693816 1.56159306 1.55384317] 1.54613174 1.53845858 1.53082351 1.52322632 1.51566684 1.50814487 93.8489825 117.27829 1.608910891 2.40138926 3.18596216 3.96268855 4.73162697 5.49283561 6.24637224 6.99229427] 7.73065871 8.46152222 9.18494104 9.90097109 10.6096679 11.3110865 750.79186843.421255 1.600985222 1.58911125 1.57732534 1.56562685 1.55401511 1.5424895 1.53104937 1.51969409 1.50842303 1.49723556 1.48613106 1.47510893 1.46416853 1.45330929 90.213643 113.191264 0.808467717 1.612947918 7.192 7.120418863 -$4.1754 -$4.0870 Bond price change: Yield 1.0-2.0% T Ct 0.5 1.625 1.616935434 0.808467717 1.608989757 7.192 7.120418863 -$8.3507 -$8.0030 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 1.625 101.625 1.608910891 1.60092617| 1.59298108 1.58507542 1.57720899 1.5693816 1.56159306 1.55384317| 1.54613174 1.53845858 1.53082351 1.52322632 1.51566684 1.50814487 93.8489825 117.27829 1.608910891 2.40138926 3.18596216 3.96268855 4.73162697 5.492835616.24637224 6.99229427| 7.73065871 8.46152222 9.18494104 9.90097109 10.6096679 11.3110865 750.79186843.421255 1.593137255 1.57744094 1.56189927 1.54651072 1.53127379 1.51618698 1.50124882 1.48645783 1.47181257 1.4573116 1.4429535| 1.42873686 1.41466029 1.40072241 86.735959 109.275302 PV (Ct) &1.000% PV(Ct)*t PV (Ct) &2.000% Duration (annual compunding) Modified duration Approx. change in bond price Actual bond price change
