The correct answer is A because the modified duration of the portfolio is calculated as the weighted average of the modified durations of the individual bonds, using market values as weights. Here's the step-by-step breakdown:

1. Calculate Modified Duration for Each Bond:

   • Modified Duration (ModDur) = Macaulay Duration / (1 + Yield to Maturity)
   • ModDur of Bond 1 = 7.5 / (1 + 4%) = 7.211538
   • ModDur of Bond 2 = 5.4 / (1 + 3%) = 5.242718

2. Determine Weights Based on Market Values:

   • Weight for Bond 1 = $200,000 / ($200,000 + $400,000) = 0.333333
   • Weight for Bond 2 = $400,000 / ($200,000 + $400,000) = 0.666667

3. Calculate Portfolio Modified Duration:

   • Portfolio ModDur = (Weight for Bond 1 × ModDur of Bond 1) + (Weight for Bond 2 × ModDur of Bond 2)
   • Portfolio ModDur = (0.333333 × 7.211538) + (0.666667 × 5.242718) = 5.898992 ≈ 5.9

Why Not B or C?

• B is incorrect because it uses par values instead of market values for weights, leading to a miscalculation.
• C is incorrect because it mistakenly uses Macaulay duration instead of modified duration for the portfolio calculation.