Question

Santiago receives ​$120 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 two times the amount invested at​ 3%. Find the amount invested at each rate.

Answer 1

Santiago invested $500 at 2%, $1,000 at 3%, and $2,000 at 4%.

Step-by-step explanation:

Let's denote the amount invested at 2% as x dollars. Then, the amount invested at 3% would be x + 500 dollars, and the amount invested at 4% would be 2 times the amount invested at 3%, which is 2(x + 500) dollars.

Now, we can use the formula for simple interest to find the total interest earned:

Total interest = (Principal * Rate * Time)

120 = (x * 0.02) + ((x + 500) * 0.03) + (2(x + 500) * 0.04)

Simplifying the equation, we get:

120 = 0.02x + 0.03(x + 500) + 0.08(x + 500)

From here, we can solve for x to find the amount invested at 2% and then calculate the amounts invested at 3% and 4%.

Multiplying out the terms, we get:

120 = 0.02x + 0.03x + 15 + 0.08x + 40

Combining like terms, we have:

120 = 0.13x + 55

Subtracting 55 from both sides, we get:

65 = 0.13x

Dividing both sides by 0.13, we find:

x = 500

Therefore, Santiago invested $500 at 2%, $(500 + 500) = $1,000 at 3%, and $2(500 + 500) = $2,000 at 4%.