Final answer:
The bond's present value is calculated by discounting its future cash flows at the respective spot rates. The total present value of the bond is $1182.77, therefore the correct answer is (d) $1182.77.
Step-by-step explanation:
To calculate the present value (PV) of a bond with a maturity of 3 years, an annual coupon of $100, and a face value of $1000, we must discount each of the bond's cash flows back to the present using the appropriate spot rates. For this bond, the cash flows would be $100 for the first two years and $1100 in the last year when the final coupon and the face value are paid.
To discount these cash flows, we use the formula PV = C / (1 + r)^t, where 'C' is the cash flow, 'r' is the spot rate appropriate for the cash flow's time period, and 't' is the time period in years. Applying this to the bond question, we get:
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- Year 1 cash flow PV: $100 / (1 + 4%) = $96.15
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- Year 2 cash flow PV: $100 / (1 + 4.5%)^2 = $91.70
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- Year 3 cash flow PV: $1100 / (1 + 4.75%)^3 = $994.92
Adding these up, the total present value of the bond is $96.15 + $91.70 + $994.92 = $1182.77.
Therefore, the correct answer is (d) $1182.77.