Argentine Float.$$The Argentine peso was fixed through a currency board at Ps$1\mathrm{.}00/$$ throughout the $1990$s$.$ In January$2002,$ the Argentine peso was floated. On January$29,2003,$ it was trading at Ps$3\mathrm{.}21/$$$.$ During that$$ one$-$year period,$$ Argentina's inflation rate was $19\%$ on an annualized basis. Inflation in the United States during that same period was $2\mathrm{.}4\%$ annualized.

a$.$ What should have been the exchange rate in January $2003$ if PPP$$ held?

b$.$ By what percentage was the Argentine peso undervalued on an annualized$$ basis?

c$.$ What were the probable causes of$$ undervaluation?