(Related to Checkpoint 9.4) (Bond valuation) A bond that matures in 15 years has a $\$ 1,000$ par value. The annual coupon interest rate is 14 percent and the market's required yield to maturity on a comparable-risk bond is 17 percent. What would be the value of this bond if it paid interest annually? What would be the value of this bond if it paid interest semiannually? a. The value of this bond if it paid interest annually would be $\$ 840.27$. (Round to the nearest cent.) b. The value of this bond if it paid interest semiannually would be $\$ \square$. (Round to the nearest cent.)

Step 1 ：Given values are: Par value of the bond is \$1000, Annual coupon interest rate is 14\%, Market's required yield to maturity is 17\%, and Years until the bond matures is 15.

Step 2 ：First, calculate the semiannual values. The semiannual coupon rate is the annual coupon rate divided by 2, which is \(0.14 / 2 = 0.07\) or 7\%. The semiannual yield is the annual yield divided by 2, which is \(0.17 / 2 = 0.085\) or 8.5\%. The number of periods is the years to maturity times 2, which is \(15 * 2 = 30\).

Step 3 ：Next, calculate the semiannual interest payment. This is the par value times the semiannual coupon rate, which is \(1000 * 0.07 = \$70\).

Step 4 ：Then, calculate the present value of the interest payments (annuity). This is the interest payment times the quantity 1 minus the quantity 1 plus the semiannual yield raised to the negative number of periods, all divided by the semiannual yield. This is \(70 * (1 - (1 + 0.085)^{-30}) / 0.085 = \$752.28\).

Step 5 ：After that, calculate the present value of the par value at maturity (lump sum). This is the par value divided by the quantity 1 plus the semiannual yield raised to the number of periods. This is \(1000 / (1 + 0.085)^{30} = \$86.52\).

Step 6 ：Finally, calculate the total value of the bond. This is the sum of the present value of the interest payments and the present value of the par value at maturity. This is \(752.28 + 86.52 = \$838.80\).

Step 7 ：So, the value of this bond if it paid interest semiannually would be \(\boxed{\$838.80}\). (Round to the nearest cent.)