Explanation

Correct Answer: B (6.41%)

Calculation Approach:

Given:

• Bond price: $975.00 (discount to $1,000 par value)
• Coupon rate: 6.0% annually
• Maturity: 8 years
• Annual coupon payment: $60 ($1,000 × 6%)

Since the bond is trading at a discount ($975 < $1,000), the YTM must be greater than the 6% coupon rate. This eliminates option A (5.88%).

YTM Calculation Logic:

The YTM is the discount rate that equates the present value of all future cash flows to the current market price:

$975 = \frac{60}{(1+YTM)^1} + \frac{60}{(1+YTM)^2} + \cdots + \frac{60}{(1+YTM)^8} + \frac{1000}{(1+YTM)^8}$

Verification:

• At 6.41% YTM, the present value of cash flows equals approximately $975
• The bond trades at a discount, so YTM > coupon rate
• Option B (6.41%) is the only rate between 6% and 7% that satisfies this condition

Key Insight: When a bond trades at a discount, YTM > coupon rate; when at a premium, YTM < coupon rate.