Explanation:
The price of a bond is the present value of its future cash flows. With a coupon rate of 7% and a face value of $100, the annual coupon payment is 7% × $100 = $7. Each cash flow must be discounted using the spot rate corresponding to its maturity:
| Year | Cash Flow | Spot Rate | Present Value |
|---|---|---|---|
| 1 | $7 | 4% | $7 / (1.04)¹ = $6.7308 |
| 2 | $7 | 5% | $7 / (1.05)² = $6.3492 |
| 3 | $7 + $100 = $107 | 5.5% | $107 / (1.055)³ = $91.1324 |
Bond Price = $6.7308 + $6.3492 + $91.1324 ≈ $104.21
The correct answer is D (104.2).
Q.3540 A 3-year bond with a face value of $100 offers a 7% coupon rate with interest paid annually. Assuming the following sequence of spot rates, the price of the bond is closest to:
| Time to Maturity | Spot Rate (%) |
|---|---|
| 1 | 4 |
| 2 | 5 |
| 3 | 5.5 |
A
102.48
B
106.74
C
103.56
D
104.2
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