Answer-first summary for fast verification
Answer: $105.62
The bond pays four semiannual coupon payments of \$4 each, plus \$100 principal at maturity. Because the spot rates are given with **continuous compounding**, each cash flow is discounted using: \[ PV = CF \times e^{-rt} \] ### Cash flows and discounting - **0.5 years:** \$4 discounted at 3.0% \[ 4e^{-0.03(0.5)} = 4e^{-0.015} \approx 3.9404 \] - **1.0 year:** \$4 discounted at 4.0% \[ 4e^{-0.04(1.0)} = 4e^{-0.04} \approx 3.8432 \] - **1.5 years:** \$4 discounted at 4.6% \[ 4e^{-0.046(1.5)} = 4e^{-0.069} \approx 3.7333 \] - **2.0 years:** \$104 discounted at 5.0% \[ 104e^{-0.05(2.0)} = 104e^{-0.10} \approx 94.1022 \] ### Total price \[ 3.9404 + 3.8432 + 3.7333 + 94.1022 \approx 105.62 \] So the nearest theoretical price is **\$105.62**, which is **D**.
Author: Manit Arora
Ultimate access to all questions.
Question 713.1. Consider the steep spot (aka, zero) rate curve illustrated below: 3.0% at 0.5 years, 4.0% at 1.0 year, 4.6% at 1.5 years and 5.0% at 2.0 years. Each of these zero rates is per annum with continuous compounding.
| Face value (aka, principal, par) | $100.00 |
|---|---|
| Semi-annual coupon (per annum) | 8.0% |
Zero (spot) rate curve
Which of the following is nearest to the theoretical price of a two-year $100.00 face value bond that pays an 8.0% semi-annual coupon (4.0% coupon every six months)?
A
$97.31
B
$99.47
C
$102.38
D
$105.62
No comments yet.