Assume that today’s 6-month spot rate is 10% and in six months the new 6-month spot rate can be either 5% or 15% with eq

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Assume that today’s 6-month spot rate is 10% and in six months
the new 6-month spot rate can be either 5% or 15% with equal
probability, so that the expected 6-month spot rate six months from
now is equal to the current 6-month spot rate and it is equal to
10%. Keep at least 7 decimal digits for all your calculations and
answers (it is important to keep such precision in this
question!!!)
a) Assume people are risk-neutral. Find the 1-year spot
rate.
b) You may notice that the answer you found in part (a is less
than 10%. i.e., the term stricture of spot rates is downward
sloping (longer rates are lower than shorter rates) while the
expected short-term spot rates remain the same. In a more realistic
scenario, term stricture of spot rates is upward sloping. So, let’s
abandon the assumption that people are risk-neutral and instead
assume that 1-year spot rate is 10.1%. Find risk-neutral
probability of an “up” move (i.e., the probability that the 6-month
spot rate will increase to 15%)
c) Do you think people in part (b) are risk-averse or
risk-loving? Explain why