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Answer: 5.00%
The correct answer is C, which represents the 2-year forward rate starting in 3 years. This forward rate is calculated using the formula: \[ 3F2 = \frac{(Rs \times 5) - (R3 \times 3)}{(5 - 3)} \] Where: - \( R3 \) is the 3-year zero rate, which is 2.50%. - \( Rs \) is the 5-year zero rate, which is 3.50%. - \( 3F2 \) is the 2-year forward rate in year 3. Plugging in the values, we get: \[ 3F2 = \frac{(3.50\% \times 5) - (2.50\% \times 3)}{2} \] \[ 3F2 = \frac{17.5\% - 7.5\%}{2} \] \[ 3F2 = \frac{10\%}{2} \] \[ 3F2 = 5\% \] This calculation shows that the 2-year forward rate starting in 3 years is 5%, which corresponds to option C. The other options are incorrect for various reasons: - Option A (3.50%) is the 5-year zero rate, not the forward rate. - Option B (4.17%) is incorrectly calculated using a misrepresented formula. - Option D (6.09%) is the result of an incorrect formula application. The explanation is based on the principles outlined in the "Financial Markets and Products" section of the reference material by the Global Association of Risk Professionals, specifically Chapter 16 on the properties of interest rates, with the learning objective to derive forward interest rates from a set of spot rates.
Author: LeetQuiz Editorial Team
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A trader is analyzing forward rates by utilizing the current term structure of continuously compounded zero rates. They have compiled the following data:
| Maturity in years | Zero rate (%) |
|---|---|
| 1 | 1.50 |
| 2 | 2.00 |
| 3 | 2.50 |
| 4 | 3.00 |
| 5 | 3.50 |
Using the above information, calculate the approximate forward rate for a period that commences in 3 years and extends for 2 years.
A
3.50%
B
4.17%
C
5.00%
D
6.09%