In country X, expected inflation per year is only 7%, but the expected variation in inflation is large. Suppose that inflation can vary within the range 3% to 19%.

a) What is the range of real rate of interest if the nominal interest rate in country X is 9%?

b) If probability of 19% inflation is 0.25 and 3% inflation is 0.75, what is the expected real rate of interest in country X?

c) What is the standard deviation of inflation and real interest rate?

d) Government of country X is thinking of issuing inflation index bonds. It aims to give the investors fixed real return equal to the expected real interest rate. It is expected to issue bonds worth $1,000,000,000.

e) What is the maximum unplanned (or excess) interest payment government of country X has to make in any given year?