Financial Risk Manager Part 1

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Explanation:

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.

Explanation:

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.

Comments (1)

Yash ParwaniMar 30, 2026 12:12 PM

The answer provided is wrong. It is said that we need to assume continuous compounding

LeetQuiz .Apr 1, 2026 10:38 AM

Hi Yash, Thanks for your comment. You're right. Assuming continuous compounding, according to the calculation, the answer is exactly 7%, the option B.

The interest rate for a 1-year period is 5% and the rate for a 2-year period is 6%. Assuming continuous compounding, what is the forward rate for the period from the end of the first year to the second year?

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Last updated: April 1, 2026 at 08:53

6.9991%

30.8%

7.0000%

69.2%

7.00009%

8.00000%