Explanation:
The theoretical price of the bond is calculated by discounting the cash flows using the spot rates. Assuming continuous compounding (standard for such FRM spot rate tables unless otherwise stated), the cash flows are semiannual coupons of \`40$ (8`\% \times \`1000` / 2$) and the principal at maturity.
Price = $40 \times e^{-0.04 \times 0.5} + 40 \times e^{-0.043 \times 1} + 40 \times e^{-0.049 \times 1.5} + 1040 \times e^{-0.055 \times 2}40\times 0.9802 + 40 \times 0.9579 + 40 \times 0.9291 + 1040 \times 0.8958$ Price =
Price
The closest value is \`1`,046$.
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Q.76 You have been given the following spot rates table:
| Maturity | Spot Rate |
|---|---|
| 0.5 year | 4.0% |
| 1 year | 4.3% |
| 1.5 years | 4.9% |
| 2 years | 5.5% |
If a 2-year bond with a principal of $1000 pays a semiannual coupon of 8% per year, then which of the following is closest to the theoretical price of the bond?
A
$1,046
B
$998
C
$1,002
D
$1,197