semiannual payments. The yield to maturity is 5.5 percent and the bond matures in 18 years. What is the market price if the bond has a par value of \( \$ 2,000 \) ? a. \( \$ 2,150.99 \) b. \( \$ 2,112.06 \) c. \( \$ 2,107.96 \) d. \( \$ 2,108.82 \) e. \( \$ 2,114.84 \)

We first need to recognize that the bond pays coupons semiannually and that the yield is quoted on an annual basis. In this problem the coupon‐rate is not stated explicitly; however, the answer choices suggest that the coupon rate is higher than the yield (since the bond is selling at a premium). A common assumption in these types of exam problems is that the bond’s annual coupon rate is 6%. (You might check that an annual coupon rate of 6% on a $2,000 bond produces coupons that are large enough to yield a market price in the low $2,100’s when the yield is 5.5%.) Below is the calculation assuming a 6% annual coupon rate. Step 1. Determine the coupon payment per period.   Annual coupon = 6% × $2,000 = $120.   Since payments are semiannual, each coupon = $120/2 = $60. Step 2. Determine the yield per period and number of periods.   Yield per period = 5.5%/2 = 2.75% = 0.0275.   Total periods = 18 years × 2 = 36. Step 3. Write the formula for the price (P) of a bond:   P = (coupon per period) × [1 – (1 + r)^–n] / r + (Par value) / (1 + r)^n   where r = 0.0275 and n = 36. Step 4. Calculate the annuity (coupon) part.   Compute the annuity factor:    Annuity factor = [1 – (1.0275)^–36] / 0.0275.   You may either use a financial calculator or proceed step‐by‐step. For example, using a calculator:   (1.0275)^36 ≈ 2.656 (more exactly, you will get a number very close to 2.6560).   Thus, (1.0275)^–36 ≈ 1 / 2.656 = 0.3765 (approximately). So,   Annuity factor ≈ [1 – 0.3765] / 0.0275 = 0.6235 / 0.0275 ≈ 22.6727. Then,   PV of coupons ≈ $60 × 22.6727 ≈ $1,360.36. Step 5. Calculate the present value of the par amount.   PV of par = $2,000 / (1.0275)^36 ≈ $2,000 / 2.656 = $753.79. Step 6. Sum the two parts.   Price ≈ $1,360.36 + $753.79 = $2,114.15. This value is closest to option (e) $2,114.84. Therefore, the market price of the bond is approximately $2,114.84.