To calculate the Macaulay duration with continuous compounding: Coupon payments are $3 every 6 months for a face value of $100. Yield (r) = 10% (0.10) continuous. Present values of cash flows at times t=0.5, t=1.0, and t=1.5: PV1 (t=0.5) = 3 × e^(-0.10 × 0.5) = 3 × 0.9512 = 2.8537 PV2 (t=1.0) = 3 × e^(-0.10 × 1.0) = 3 × 0.9048 = 2.7145 PV3 (t=1.5) = 103 × e^(-0.10 × 1.5) = 103 × 0.8607 = 88.6530 Total Present Value (Price) = 2.8537 + 2.7145 + 88.6530 = 94.2212 Duration = Σ [t × PV(t)] / Total PV = [(0.5 × 2.8537) + (1.0 × 2.7145) + (1.5 × 88.6530)] / 94.2212 = [1.42685 + 2.7145 + 132.9795] / 94.2212 = 137.1208 / 94.2212 ≈ 1.4553 years.