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Answer: c) 4.88%
**Correct answer: C) 4.88%** The bond’s price is found by discounting each cash flow using the given spot rates, and then the yield-to-maturity is the single semi-annual-compounded rate that matches that price. ### 1) Bond cash flows - Every 6 months: coupon = 3.0% of $100 = **$3.00** - At maturity (2 years): final cash flow = **$103.00** ### 2) Discount using spot rates Using the annual spot rates with annual compounding: - 0.5y: $3 / (1.02)^{0.5}$ - 1.0y: $3 / (1.036)^{1.0}$ - 1.5y: $3 / (1.044)^{1.5}$ - 2.0y: $103 / (1.05)^{2.0}$ This gives a bond price of approximately **$102.10**. ### 3) Solve for YTM on a semi-annual basis Now solve for the semi-annual yield that prices the bond at about $102.10. The yield comes out to: \[ \text{YTM} \approx 4.884\% \] ### Intuition Because the coupon rate (6%) is above the long-term spot rate (5%), the bond trades above par, so its yield must be **below 5.0%**. The nearest choice is therefore **4.88%**.
Author: Manit Arora
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Q-713.2. Consider the steep spot (aka, zero) rate curve illustrated below: 2.0% at 0.5 years, 3.60% at 1.0 year, 4.40% at 1.5 years and 5.0% at 2.0 years. Each of these zero rates is per annum with annual compounding.
| Face value; aka, principal, par | $100.00 |
|---|---|
| Semi-annual coupon (per annum) | 6.0% |
We are interested in the yield-to-maturity (aka, yield) of a two-year $100.00 face value bond that pays an 6.0% semi-annual coupon (3.0% coupon every six months). If this yield-to-maturity is expressed with semi-annual compounding (aka, bond equivalent basis), which of the following is nearest to this yield?
A
a) 2.52%
B
b) 3.95%
C
c) 4.88%
D
d) 5.00%
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