"Suppose we observe the three-year Treasury security rate (1R3) to be 12%, the expected one-year rate next year -E(2R1)- to be 8%, and the expected one-year rate the following year -E(3R1)- to be 10%. If the unbiased expectation theory of the term structure holds, what is the one-year Treasury security rate?

Help! I've done this problem over 5 times and I keep getting ~30% but the answer to the problem is 18%. However I have to show how to get 18%.

Any help is appreciated!!

Also, if you guys may, this one too.

"Interest rates on 5-year Treasury securities are currently 8%, while the 8-year Treasury securities yield 10%. If the pure expectations theory is correct, what does the market believe that 3-year securities will be yielding 5 years from now?"

I have no idea how to do this one!