Kasey Corp. has a bond outstanding with a coupon rate of 6.04 percent and semiannual payments. The bond has a yield to maturity of 6.1 percent, a par value of \( \$ 2,000 \), and matures in 15 years. What is the quoted price of the bond? a. \( 2,187.15 \) b. 99.70 c. 99.42 d. 101.40 e. \( 1,988.32 \)

To find the quoted price of the bond, we can use the formula for the present value of a bond: \[ PV = \frac{PMT}{r} \left( 1 - \frac{1}{(1 + r)^n} \right) + \frac{FV}{(1 + r)^n} \] where: - \( PV \) is the present value (quoted price) of the bond - \( PMT \) is the semiannual coupon payment - \( r \) is the semiannual yield to maturity - \( n \) is the number of semiannual periods until maturity - \( FV \) is the face value of the bond Given: - Coupon rate = 6.04% - Yield to maturity = 6.1% - Par value = $2,000 - Maturity in 15 years First, we need to calculate the semiannual coupon payment and the semiannual yield to maturity. 1. Semiannual coupon payment: \[ PMT = \frac{6.04\% \times \$2,000}{2} = \$60.40 \] 2. Semiannual yield to maturity: \[ r = \frac{6.1\%}{2} = 3.05\% \] 3. Number of semiannual periods until maturity: \[ n = 15 \times 2 = 30 \] 4. Face value of the bond: \[ FV = \$2,000 \] Now, we can substitute these values into the formula to find the quoted price of the bond. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{60.4}{0.0305}\right)\left(1-\left(\frac{1}{\left(1+0.0305\right)^{30}}\right)\right)+\left(\frac{2000}{\left(1+0.0305\right)^{30}}\right)\) - step1: Divide the terms: \(\frac{120800}{61}\left(1-\left(\frac{1}{\left(1+0.0305\right)^{30}}\right)\right)+\left(\frac{2000}{\left(1+0.0305\right)^{30}}\right)\) - step2: Add the numbers: \(\frac{120800}{61}\left(1-\left(\frac{1}{1.0305^{30}}\right)\right)+\left(\frac{2000}{\left(1+0.0305\right)^{30}}\right)\) - step3: Convert the expressions: \(\frac{120800}{61}\left(1-\left(\frac{1}{\left(\frac{2061}{2000}\right)^{30}}\right)\right)+\left(\frac{2000}{\left(1+0.0305\right)^{30}}\right)\) - step4: Simplify: \(\frac{120800}{61}\left(1-\frac{2000^{30}}{2061^{30}}\right)+\left(\frac{2000}{\left(1+0.0305\right)^{30}}\right)\) - step5: Subtract the numbers: \(\frac{120800}{61}\times \frac{2061^{30}-2000^{30}}{2061^{30}}+\left(\frac{2000}{\left(1+0.0305\right)^{30}}\right)\) - step6: Add the numbers: \(\frac{120800}{61}\times \frac{2061^{30}-2000^{30}}{2061^{30}}+\left(\frac{2000}{1.0305^{30}}\right)\) - step7: Convert the expressions: \(\frac{120800}{61}\times \frac{2061^{30}-2000^{30}}{2061^{30}}+\left(\frac{2000}{\left(\frac{2061}{2000}\right)^{30}}\right)\) - step8: Simplify: \(\frac{120800}{61}\times \frac{2061^{30}-2000^{30}}{2061^{30}}+\frac{2000^{31}}{2061^{30}}\) - step9: Multiply the numbers: \(\frac{120800\times 2061^{30}-120800\times 2000^{30}}{61\times 2061^{30}}+\frac{2000^{31}}{2061^{30}}\) - step10: Reduce fractions to a common denominator: \(\frac{120800\times 2061^{30}-120800\times 2000^{30}}{61\times 2061^{30}}+\frac{2000^{31}\times 61}{2061^{30}\times 61}\) - step11: Reorder the terms: \(\frac{120800\times 2061^{30}-120800\times 2000^{30}}{61\times 2061^{30}}+\frac{2000^{31}\times 61}{61\times 2061^{30}}\) - step12: Transform the expression: \(\frac{120800\times 2061^{30}-120800\times 2000^{30}+2000^{31}\times 61}{61\times 2061^{30}}\) - step13: Reorder the terms: \(\frac{120800\times 2061^{30}-120800\times 2000^{30}+61\times 2000^{31}}{61\times 2061^{30}}\) - step14: Add the numbers: \(\frac{120800\times 2061^{30}+1200\times 2000^{30}}{61\times 2061^{30}}\) The quoted price of the bond is approximately $1,988.32.