Spot Rates question

An analyst collects the following information regarding the spot rates of interest: 1-year rate = 4% 2-year rate = 5% 3-year rate = 6% 4-year rate = 7% Utilizing the pure expectations theory of the term structure of interest rates, the expected annualized 2-year interest rate two years from today is closest to: a. 7.02% b. 8.03% c. 9.04% The answer has the calculation for the exact answer and also a calculation for an approximation (which leads you to the correct answer.) Can someone please explain his/her answer? Thanks.

((1 + x)^2) * ((1+.05)^2)=(1+.07)^4 x=9.04 OR ((7*4)-(5*2))/2=9 Is that the answer? If so, this comes from the forward/spot section

I got 9.04 as well. (1.07)^4 / (1.05)^2 = 1.3108/1.1025 =1.1889 18.89% is for two years, so: =1.1889^.5 =1.0904= 9.04%

Yep, 9.04% is the answer.

Can someone explain why you use the 4 and the 2 year rates and not the 3 and the 1 year rates. I thought it just had to be a 2 year difference 4-2=2 and 3-1=2

Because we are looking for 2f2, the years of interest are 2 and 2+2.