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

₀i₁=3.5%, ₀i₂=4%, ₀i₆=5%, ₀i₁₀=6% and ₀i₁₂=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 ₂i^e₈ implicit in the above term structure. Answer the question assuming monthly compounding.

Explain all the steps of your argumentation and show all the details of your calculations.

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