The nominal interest rate on $3-$year car loan $($fixed payment loan$)$ is set at $5\mathrm{.}5\%.$ When the loan contract is signed, the inflation rate was expected to be $2\%.$ Immediately after the loan contract is signed by the borrower and the lender, the inflation rate falls to $1\mathrm{.}5\%.[5$ points$]$ a$)$ Compute the ex post real interest rate. b$)$ Compute the ex ante real interest rate. c$)$ Who is better off as a result of the unexpected change in inflation? Explain how you know.