Answer: 7.0000%

The correct answer is **B: 7.0000%**. ### Explanation For **continuously compounded** spot rates, the forward rate from time \( t_1 \) to \( t_2 \) is derived from the no-arbitrage relationship: \[ e^{r_2 \cdot t_2} = e^{r_1 \cdot t_1} \cdot e^{f \cdot (t_2 - t_1)} \] Taking the natural log on both sides and solving for the forward rate \( f \): \[ f = \frac{r_2 \cdot t_2 - r_1 \cdot t_1}{t_2 - t_1} \] Here: - \( r_1 = 5\% = 0.05 \) (1-year spot rate), so \( t_1 = 1 \) - \( r_2 = 6\% = 0.06 \) (2-year spot rate), so \( t_2 = 2 \) - Forward period: from year 1 to year 2 (\( t_2 - t_1 = 1 \)) Plugging in the values: \[ f = \frac{0.06 \times 2 - 0.05 \times 1}{2 - 1} = \frac{0.12 - 0.05}{1} = 0.07 = 7.0000\% \] This is exactly 7% (the slight floating-point difference in computation is negligible and rounds precisely to 7.0000%). ### Why the other options are incorrect: - **A (6.9991%)** and **C (7.00009%)**: These appear to be distractors from rounding errors or confusion with discrete compounding formulas. - **D (8.00000%)**: This might result from mistakenly using the discrete compounding forward rate formula or arithmetic averaging without proper weighting. **Key takeaway for FRM Part 1**: With **continuous compounding**, the forward rate is simply the weighted difference of the spot rates (no need for the more complex \((1 + r_2)^{t_2} / (1 + r_1)^{t_1} - 1\) formula used in annual or semi-annual compounding). This makes calculations cleaner and exact in this case.

Author: LeetQuiz .