Answer: USD 15.98

## Explanation This question involves calculating the price difference between two bonds with different coupon rates but the same yield to maturity and maturity. **Given:** - Bond X: 10% annual coupon, 5-year maturity, YTM = 8% - Bond Y: 6% annual coupon, 5-year maturity, YTM = 8% - Face value: USD 100 for both **Step 1: Calculate Bond X price** Bond X pays USD 10 annually for 5 years, plus USD 100 at maturity. Price_X = 10/(1.08) + 10/(1.08)² + 10/(1.08)³ + 10/(1.08)⁴ + 10/(1.08)⁵ + 100/(1.08)⁵ Using present value formula: PV of coupons = 10 × [1 - (1.08)^{-5}] / 0.08 = 10 × 3.99271 = 39.9271 PV of face value = 100 / (1.08)⁵ = 100 / 1.46933 = 68.0583 Price_X = 39.9271 + 68.0583 = 107.9854 ≈ USD 107.99 **Step 2: Calculate Bond Y price** Bond Y pays USD 6 annually for 5 years, plus USD 100 at maturity. PV of coupons = 6 × [1 - (1.08)^{-5}] / 0.08 = 6 × 3.99271 = 23.9563 PV of face value = 68.0583 (same as above) Price_Y = 23.9563 + 68.0583 = 92.0146 ≈ USD 92.01 **Step 3: Calculate price difference** Difference = Price_X - Price_Y = 107.99 - 92.01 = USD 15.98 Therefore, the price difference is USD 15.98, which corresponds to option A. **Key Insight:** When two bonds have the same YTM and maturity, the bond with the higher coupon rate will trade at a premium relative to the bond with the lower coupon rate. This is because the higher coupon bond provides more cash flows in the earlier years, which are more valuable when discounted at the same rate.

Author: LeetQuiz Editorial Team