Question

Santiago receives ​$179 per year in simple interest from three investments. Part is invested at​ 2%, part at​ 3%, and part at​ 4%. There is​ $500 more invested at​ 3% than at​ 2%. The amount invested at​ 4% is four times the amount invested at​ 3%. Find the amount invested at each rate.

Answer 1

Santiago invested $2,000 at 2% interest, $2,500 at 3% interest, and $10,000 at 4% interest.

Let's assume that Santiago invested x amount at 2% interest, y amount at 3% interest, and z amount at 4% interest.

We are given that y = x + $500, and z = 4y.

We know that the total interest earned is $179, so we can write the equation 0.02x + 0.03y + 0.04z = $179.

Substituting the values of y and z from step 1 into the equation from step 2, we get 0.02x + 0.03(x + $500) + 0.04(4(x + $500)) = $179.

By simplifying and solving the equation, we find that x = $2,000, y = $2,500, and z = $10,000.

Therefore, Santiago invested $2,000 at 2% interest, $2,500 at 3% interest, and $10,000 at 4% interest.