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(25 Points) 3. Suppose today you purchase a seven-year, 5 percent coupon bond (paid annually) that is priced to yield 7.38 percent. a. Given, the price and duration of the bond: Seven-yearBondi Par value-$1,000 Coupon rate-5% Annual payments r 7.38% Maturity- 7 years 1.000 50.000 0.931 46.564 46.564 2.000 50.000 0.867 43.363 86.727 3.000 50.000 0.808 40.383 121.149 4.000 50.000 0.752 37.608 150.431 5.000 50.000 0.700 35.023 175.115 6.000 50.000 0.652 32.616 195.696 7.000 1050.000 0.607 637.860 4465.021 Sum 873417 5240.702 Duration= 6.000 b. Show that if market yields (interest rates) rise to 8 percent on the day after purchasing the bond (just my luck), the bond that purchased to yield 7.38% (YTM of 7.38%) and your client's investment horizon (date of planned liquidation) is 6.00 years (Duration of the bond), show that your client will still earn a 7.38 percent yield on his/her investment. Value of bond at end of 6.0 years: PV = ($50+$1,000) ( 1.08)-1-s Future value of interest payments at end of 6 years:-s or Future value of interest payments at end of 6 years0 Future value of all cash flows at n- 6 years: 0.08 Coupon interest payments over six years PV Interest on interest Value of bond at end of year six Total future value of investment Annual Compound Yield on bond at the end of 6 years: (1 +r)"-s_ __--r-0.0738 or 7.38%, which was the initial YTM on the bond

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