3. Suppose today you purchase a seven-year maturity, 5 percent coupon bond (paid annually) that is priced to yield 7.38 percent. a. The price and duration of the bond are: Seven-year Bond: Par value $1,000 Coupon rate-5% Annual payments r-7.38% CF Maturity-7 years 1.000 50.000 2.000 50.000 3.000 50.000 4.00050.000 5.000 50.000 6.000 50.000 7.000 1050.000 0.931 0.867 0.808 0.752 0.700 0.652 46.564 46.564 43.363 86.727 40.383 121.149 37.608 150.431 35.023 175.115 32.616 195.696 0.607 637.860 4465.021 Sum P$873.417 5240.702 Duration 6.000 b. Ifinterest rates rise to 8 percent the day after you purchase and remain at 8 percent, show that the bond that initially had a YTM of 7.38% and your investment horizon is 6.00 years (Duration of the bond), show that you will still earn a 7.38 percent yield on vour investment over vour time horizon of 6 vears. Value of bond at end of 6.0 years: PV -(S50+S1,000 (1.08)-S Future value of interest payments at end of 6 years: - S221.48* Future value of interest payments at end of 6 years: 50 +0.08)6-1 Future value of all cash flows at n = 6 years: S300.00 66.80 Coupon interest payments over six years Interest on interest at 5 percent Value of bond at end of year four Total future value of investment Yield on bond at the end of 6 years: $873.417(1 +r)" = $ -r-0.0738 or 7.38%, which was the bond's initial YTM