Juan has a capital of $530,000, if he invests a certain amount at 2% and another amount at 4%, for the two investments he obtains $16,200. How much did you invest at each interest rate?

Let x be the amount invested in the 2% interest and y be the amount invested in the 4% interest. Then, we have the equation $$ 0.02x+0.04y=16200\:\xrightarrow{}\:2x+4y=1620000 $$. Moreover, the total amount to be invested is $530000. So, we also have the equation $$ x+y=530000 $$. Using these two equations and the process of elimination or substitution, we get$$ x=250000,\:y=280000 $$. Answer: $250,000 was invested for the 2% interest; $280,000 was invested for the 4% interest.