jmc

After two years, at a four percent annual interest rate, the Jose's investment will have grown to $50000\cdot 1.04^2=54080$. Patricia has the same annual interest rate, but compounded quarterly, so each quarter (or each period of three months), her investment is compounded at the rate of $4/4=1$ percent. In two years, there are eight quarters, so Patricia's investment will have grown to $50000\cdot 1.01^8=54143$, to the nearest dollar. The difference is then $54143-54080=\boxed{63}$.