I am not able to replicate the chart for a 30 year bond using the example from the previous page. INTEREST RATE RISKPg 169the amount of risk a bond has is dependant on0 remaining time to maturity.2 coupon rateGENERAL RULE4the longer the maturity the greater the interest rate riskthe lower the coupon rate, the the risk(1)QWHY?Figure 6.2par = 1,000coupon rate=t10 compounded sem. annually.current rate=05 = a × 62syield 1,000,10 = 100/2 = $50step 1 PU of 1,000 in 30 years atFU1,000PV = (H)step 2= PV of a "so annuityAnnuity PV =(17.025) 60Co •1- (1+r) +-- [ ]. [+- (lota]·025Current value of bond =50=+05/2[227.28= 14545.431772/71book answer11768.629EXAMPLE6.1 Semiannual Couponsin practice, bonds issued in the United States usually make coupon payments twice a year. So, if anordinary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, butthis $140 will come in two payments of $70 each. Suppose we are examining such a bond. Theyield to maturity is quoted at 16 percent.Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period multplied by the number of periods. In this case, with a 16 percent quoted yield and semiannual payments, the true yield is 8 percent per six months. The bond matures in seven years What is thebond's price? What is the effective annual yield on this bond?Based on our discussion, we know that the bond will sell at a discount because it has a coupon rate of 7 percent every six months when the market requires 8 percent every six months. So, ifour answer is equal to or exceeds $1,000, we know that we have made a mistake.To get the exact price, we first calculate the present value of the bond's face value of $1,000paid in seven years. This seven-year period has 14 periods of six months each. At 8 percent perperiod, the value is:Present value $1,000/1.08 $1,000/2.9372 = $340.46The coupons can be viewed as a 14-period annuity of $70 per period. At an 8 percent discount rate,the present value of such an annuity isAnnuity present value = $70 x (1-1/1.08.08=$70 x (1-3405.08-$70 x 8.2442-$57710The total present value gives us what the bond should sell for:170Total present value-$340.46 +57710-$917.56To calculate the effective yield on this bond, note that 8 percent every six months is equivalent toEffective annual rate= (1+08-1-16.64%The effective yield, therefore, is 16.64 percentFIGURE 6.2Interest rate risk andtime to maturityslope ofline is,much steeperPART 4CHAPTER 6Bondvalue (5)2,000Valuing Stocks and Bonds1.5001,000500$1,768.62)Interest Rates and Bond Valuation$1,047.6230-year bond11-year bondInterest Rate5%$916.67$502.11Interestrate (%)1520Value of a Bond with a 10 Percent Coupon Rate for Different Interest Rates and MaturitiesTime to Maturity30 Years$1.768.621 Year$1,047.62

Question

I am not able to replicate the chart for a 30 year bond using the example from the previous page. INTEREST RATE RISKPg 169the amount of risk a bond has is dependant on0 remaining time to maturity.2 coupon rateGENERAL RULE4the longer the maturity the greater the interest rate riskthe lower the coupon rate, the the risk(1)QWHY?Figure 6.2par = 1,000coupon rate=t10 compounded sem. annually.current rate=05 = a × 62syield 1,000,10 = 100/2 = $50step 1 PU of 1,000 in 30 years atFU1,000PV = (H)step 2= PV of a &#34;so annuityAnnuity PV =(17.025) 60Co •1- (1+r) +-- [ ]>. [+- (lota]·025Current value of bond =50=+05/2[227.28= 14545.431772/71book answer11768.629EXAMPLE6.1 Semiannual Couponsin practice, bonds issued in the United States usually make coupon payments twice a year. So, if anordinary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, butthis $140 will come in two payments of $70 each. Suppose we are examining such a bond. Theyield to maturity is quoted at 16 percent.Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period multplied by the number of periods. In this case, with a 16 percent quoted yield and semiannual payments, the true yield is 8 percent per six months. The bond matures in seven years What is thebond's price? What is the effective annual yield on this bond?Based on our discussion, we know that the bond will sell at a discount because it has a coupon rate of 7 percent every six months when the market requires 8 percent every six months. So, ifour answer is equal to or exceeds $1,000, we know that we have made a mistake.To get the exact price, we first calculate the present value of the bond's face value of $1,000paid in seven years. This seven-year period has 14 periods of six months each. At 8 percent perperiod, the value is:Present value $1,000/1.08 $1,000/2.9372 = $340.46The coupons can be viewed as a 14-period annuity of $70 per period. At an 8 percent discount rate,the present value of such an annuity isAnnuity present value = $70 x (1-1/1.08.08=$70 x (1-3405.08-$70 x 8.2442-$57710The total present value gives us what the bond should sell for:170Total present value-$340.46 +57710-$917.56To calculate the effective yield on this bond, note that 8 percent every six months is equivalent toEffective annual rate= (1+08-1-16.64%The effective yield, therefore, is 16.64 percentFIGURE 6.2Interest rate risk andtime to maturityslope ofline is,much steeperPART 4CHAPTER 6Bondvalue (5)2,000Valuing Stocks and Bonds1.5001,000500$1,768.62)Interest Rates and Bond Valuation$1,047.6230-year bond11-year bondInterest Rate5%$916.67$502.11Interestrate (%)1520Value of a Bond with a 10 Percent Coupon Rate for Different Interest Rates and MaturitiesTime to Maturity30 Years$1.768.621 Year$1,047.62

Accepted Answer

Bonds are fixed-income assets that serve as a representation of investor loans to borrowers…

Bond value (5) 2,000 1.500 1,000 500 $1,768.62) $1,04762 30-year bond 1-year bond $916.67 Interest Rate $502.11 Interest 19 15 20 rate (%) Value of a Bond with a 10 Percent Coupon Rate for Different interest Pites and Maturities Time to Maturity 1 Year $1,047.62 30 Years $1.768.62