Compute the initial price of a futures contract on the same ZCB. The futures contract has an expiration of  t = 4

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Ten Year Zero-Coupon Bond 2 3 10 10 100 9. 89.45 100 81.58 91.20 100 75.68 79.46 84.53 92.69 100 6. 71.26 87.06 93.93 100 67.97 75.62 82.74 89.22 94.98 100 65.56 72.74 79.45 85.57 91.05 95.86 100 3. 63.84 70.62 76.95 82.76 87.97 92.58 96.58 100 2 62.68 69.10 75.10 80.62 83.78 86.47 85.59 88.01 90.01 93.87 97.19 100 61.97 68.07 73.78 79.03 91.72 94.94 97.69 100 61.62 67.44 72.88 77.89 82.42 90.05 93.16 95.83 98.10 100 Short-Rate Lattice 2 3 4 8 10 10 12.97% 9. 11.79% 10.61% 10.72% 9.65% 8.68% 7 9.74% 8.77% 7.89% 7.10% 8.86% 7.97% 7.17% 6.46% 5.81% 8.05% 7.25% 6.52% 5.87% 5.28% 4.75% 4 7.32% 6.59% 5.93% 5.34% 4.80% 4.32% 3.89% 3 6.66% 5.99% 5.39% 4.85% 4.37% 3.93% 3.54% 3.18% 2 6.05% 5.45% 4.90% 4.41% 3.97% 3.57% 3.22% 2.89% 2.60% 5.50% 4.95% 4.46% 4.01% 3.61% 3.25% 2.92% 2.63% 2.37% 2.13% 5.00% 4.50% 4.05% 3.65% 3.28% 2.95% 2.66% 2.39% 2.15% 1.94% 1.74% A Bond Future Coupon 10.0% Maturity 4 1 3 4 4 104.83 3 106.09 107.36 2 107.26 108.43 109.50 108.34 109.41 110.40 111.30 109.33 110.32 111.23 112.05 112.81 Ten Year Zero-Coupon Bond 2 3 10 10 100 9. 89.45 100 81.58 91.20 100 75.68 79.46 84.53 92.69 100 6. 71.26 87.06 93.93 100 67.97 75.62 82.74 89.22 94.98 100 65.56 72.74 79.45 85.57 91.05 95.86 100 3. 63.84 70.62 76.95 82.76 87.97 92.58 96.58 100 2 62.68 69.10 75.10 80.62 83.78 86.47 85.59 88.01 90.01 93.87 97.19 100 61.97 68.07 73.78 79.03 91.72 94.94 97.69 100 61.62 67.44 72.88 77.89 82.42 90.05 93.16 95.83 98.10 100 Short-Rate Lattice 2 3 4 8 10 10 12.97% 9. 11.79% 10.61% 10.72% 9.65% 8.68% 7 9.74% 8.77% 7.89% 7.10% 8.86% 7.97% 7.17% 6.46% 5.81% 8.05% 7.25% 6.52% 5.87% 5.28% 4.75% 4 7.32% 6.59% 5.93% 5.34% 4.80% 4.32% 3.89% 3 6.66% 5.99% 5.39% 4.85% 4.37% 3.93% 3.54% 3.18% 2 6.05% 5.45% 4.90% 4.41% 3.97% 3.57% 3.22% 2.89% 2.60% 5.50% 4.95% 4.46% 4.01% 3.61% 3.25% 2.92% 2.63% 2.37% 2.13% 5.00% 4.50% 4.05% 3.65% 3.28% 2.95% 2.66% 2.39% 2.15% 1.94% 1.74% A Bond Future Coupon 10.0% Maturity 4 1 3 4 4 104.83 3 106.09 107.36 2 107.26 108.43 109.50 108.34 109.41 110.40 111.30 109.33 110.32 111.23 112.05 112.81