Answer-first summary for fast verification
Answer: 5.00%
The 2-year forward rate starting in 3 years is calculated using the formula: $$_3F_2 = \frac{(R_5 \times 5 - R_3 \times 3)}{(5 - 3)}$$ Where: - $R_3 = 3\text{-year zero rate} = 2.50\%$ - $R_5 = 5\text{-year zero rate} = 3.50\%$ - $_3F_2 = \text{2-year forward rate in year 3}$ Calculation: $$_3F_2 = \frac{(3.50\% \times 5 - 2.50\% \times 3)}{(5 - 3)} = \frac{(17.50\% - 7.50\%)}{2} = \frac{10\%}{2} = 5.00\%$$ **Why other options are incorrect:** - **A (3.50%)**: This is the zero rate (spot rate) for a 5-year investment, not the forward rate. - **B (4.17%)**: This would be the annualized 3-year forward rate starting in 2 years, calculated using the wrong formula: $_3F_2 = \frac{(R_5 \times 5 - R_3 \times 2)}{(5 - 2)}$. - **D (6.09%)**: This results from applying the wrong formula: $(1 + _3R_2) = (1 + R_5) \times (1 + R_3)$.
Author: LeetQuiz Editorial Team
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The following table provides information on the current term structure of zero (spot) rates:
| Maturity in Years | Zero Rate (%) |
|---|---|
| 1 | 1.50 |
| 2 | 2.00 |
| 3 | 2.50 |
| 4 | 3.00 |
| 5 | 3.50 |
Which of the following is closest to the 2-year forward swap rate starting in 3 years?
A
3.50%
B
4.17%
C
5.00%
D
6.09%