If the 3-year spot rate is 10.5% and the 2-year spot rate is 10%, what is the one-year forward rate of interest two years from now?
A) 3.7%
B) 9.5%
C) 11.5%
D) None of the above

Question

Quizplus · Accepted Answer

To calculate the one-year forward rate of interest two years from now, we can use the formula:

(1 + r3)^3 = (1 + r1)^1 * (1 + f2)^2

where r3 is the 3-year spot rate, r1 is the 1-year spot rate, and f2 is the one-year forward rate of interest two years from now.

Substituting the values given in the question, we get:

(1 + 0.105)^3 = (1 + r1)^1 * (1 + f2)^2

(1.105)^3 = (1 + r1) * (1 + f2)^2

1 + r1 = (1.105)^3 / (1 + f2)^2

Now, we need to solve for f2. Rearranging the above equation, we get:

1 + f2 = (1.105)^3 / (1 + r1)^(1/2)

f2 = [(1.105)^3 / (1 + r1)^(1/2)] - 1

Assuming the 1-year spot rate to be equal to or close to the 2-year spot rate, we can use the 2-year spot rate (10%) as an estimate for r1:

f2 = [(1.105)^3 / (1 + 0.10)^(1/2)] - 1

f2 ≈ 0.115 or 11.5%

Therefore, the answer is (C) 11.5%.

If the 3-Year Spot Rate Is 10