1 year Treasury rates are 4 while 2 year Treasury rates are

1 year Treasury rates are 4%, while 2 year Treasury rates are 9%. What is the expected 1 year Treasury rate one year from today? answer format: show your answer to one decimal places. If your answer is, for example, 3.252%, then input 3.3 without the percent sign.

Solution

1-year Treasury Stock, r₁ = 4%
2-year Treasury Stock, r₂ = 9%

Let 1-year Treasury Rate one year from now be ₁r₁

(1 + r₁) * (1 + ₁r₁) = (1 + r₂)^2
(1 + 0.04) * (1 + ₁r₁) = (1 + 0.09)^2
1.04 * (1 + ₁r₁) = 1.09^2
1.04 * (1 + ₁r₁) = 1.1881
1 + ₁r₁ = 1.1424
₁r₁ = 0.1424 = 14.24%

So, expected 1-year Treasury Rate one year from now is 14.24%