$1.)$ Product $"$P$"$ is produced in the U$.$S$.$ and Brazil. P is sold for $$20$ in the U$.$S$.$ and BRL$.42$ in Brazil.

a$)$ Based on the above information, what should the spot rate of the Brazilian Real $($BRL$)$ be$?$ Specify the parity relation that supports your answer. $(5$ points$)$

b$)$ One year later, the price of P would increase to $$22$ in the U$.$S$.$ and BRL$.50$ in Bracil. Given your answer in a$),$ and an interest rate of $14\%$ in the U$.$S$.,$ what must be the interest rate in Brazal? Specify the parity relation used to answer the question. $(5$ points$)$