One-Year Forward Rate Calculation: CFA Level 1 Exam Answer

Explanation

E

To calculate the one-year forward rate two years from now, we can use the relationship between spot rates and forward rates. The formula for calculating the forward rate is as follows:

(1 + forward rate)^n = (1 + spot rate)^t / (1 + spot rate)^s

Where:

• "forward rate" represents the interest rate for a future period.
• "n" represents the length of the forward period.
• "spot rate" represents the interest rate for the current period.
• "t" represents the end period.
• "s" represents the start period.

In this case, we are given the 4-year spot rate, which is 7.5%. We want to calculate the one-year forward rate two years from now, which means our start period is year 2 (the end of the 2nd year) and our end period is year 3 (the end of the 3rd year). Therefore, s = 2, t = 3, and n = 1.

Let's plug the values into the formula:

(1 + forward rate)^1 = (1 + 7.5%)^3 / (1 + 7.5%)^2

To solve for the one-year forward rate, we need to isolate (1 + forward rate) on one side of the equation. Let's rearrange the formula:

(1 + forward rate) = [(1 + 7.5%)^3 / (1 + 7.5%)^2]^(1/1)

Now we can calculate the value on the right side of the equation:

(1 + forward rate) = (1.075^3 / 1.075^2)^1

(1 + forward rate) = (1.23090625 / 1.16625)^1

(1 + forward rate) = 1.0548^1

(1 + forward rate) = 1.0548

To find the forward rate, we subtract 1 and convert it to a percentage:

forward rate = 1.0548 - 1 = 0.0548 = 5.48%

Therefore, the one-year forward rate two years from now is 5.48%.

However, none of the provided answers match this calculation. It's possible that there was an error in the question or the answer choices.