The current spot rates (annualized) for maturities expressed in months are:

₀i₁=3.5%, ₀i₂=4%, ₀i₄=5%, ₀i₁₀=6% and ₀i₁₁=6.5%.

The first subscript refers to the starting date of the investment while the second subscript refers to the term/maturity of the investment. [Note that the second subscript is NOT a date but a length.]

Assuming that the expectations theory of interest rates holds, derive the market expectations ₄i^e₇ implicit in the above term structure. Answer the question assuming monthly compounding.

Explain all the steps of your argumentation as well as the theory you use and show all the details of your calculations. Interpret your result.