The current 1-year spot rate is 6.5%, the current 2-year spot rate is 8.5% and the current 3-year spot rate is 11.8%. The 1 year forward rate two years from now is closest to…Select one:a.18.71%b.17.71%c.71.17%d.81.71%
Question
The current 1-year spot rate is 6.5%, the current 2-year spot rate is 8.5% and the current 3-year spot rate is 11.8%. The 1 year forward rate two years from now is closest to…Select one:a.18.71%b.17.71%c.71.17%d.81.71%
Solution
To find the 1-year forward rate two years from now, we can use the formula for forward rates, which is:
(1 + z_n)^n / (1 + z_m)^m = 1 + f_m,n
where:
- z_n is the n-year spot rate
- z_m is the m-year spot rate
- f_m,n is the m-year forward rate n years from now
In this case, we want to find the 1-year forward rate two years from now (f_2,1), so we have:
(1 + z_3)^3 / (1 + z_2)^2 = 1 + f_2,1
Substituting the given values:
(1 + 0.118)^3 / (1 + 0.085)^2 = 1 + f_2,1
Solving this equation gives:
f_2,1 = (1.118^3 / 1.085^2) - 1
f_2,1 = 1.1871 - 1
f_2,1 = 0.1871 or 18.71%
So, the 1-year forward rate two years from now is closest to 18.71%. Therefore, the correct answer is a. 18.71%.
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