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Answer:
Note: <em>The complete question is attached as picture below</em>
1a. The one year spot rate can be calculated using the one year zero bond.
PV * (1 + S1) = FV
1 + S1 = 1000 / 900
S1 = 1.1111 - 1
S1 = 0.1111
S1 = 11.11%
1b. PV of the 2 year bond = $950
Annual coupon = 1000 * 5% = $50
950 = 50 / (1 + S1) + (50 + 1000) / (1 + S2)^2
950 = 50 / 1.1111 + 1,050 / (1 + S2)^2
1,050/ (1 + S2)^2 = 950 - 45 = 905
(1 + S2)^2 = 1050 / 905
1 + S2 = 1.160221/2
S2 = 7.714%
1c. Price of the 2 year zero bond = 1,000 / (1 + 0.07714)^2
Price of the 2 year zero bond = 1,000 / 1.1602
Price of the 2 year zero bond = 861.9203586
Price of the 2 year zero bond = $861.92
