The correct answer is A (4.2%).

Explanation:

When fixed-rate bonds are not actively traded, the market discount rate can be estimated using matrix pricing, which involves interpolating between the yields of comparable bonds with similar credit quality and maturities. In this case, linear interpolation is the appropriate method.

Using the yields of Bond 1 (3 years, 3.4%) and Bond 2 (8 years, 5.4%), the estimated market discount rate for a 5-year bond is calculated as follows:

$$\text{Estimated Rate} = 0.034 + \left(\frac{5 - 3}{8 - 3}\right) \times (0.054 - 0.034) = 0.034 + \left(\frac{2}{5}\right) \times 0.02 = 0.042 = 4.2\%$$

• Option B (4.4%) is incorrect because it uses a simple average of the yields, which is not the correct method for interpolation.
• Option C (4.6%) is incorrect because it incorrectly applies linear interpolation from the wrong end of the interval.