Question

You invest $15000, a portion earning a simple interest rate of 2.5% per year and the rest earning a rate of 1.5% per. After one year, the total interest earned on these investments was $350. How much money did you invest at each rate? Then solve. Please identify how much at each rate.

Answer 1

By setting up a system of equations, we can determine that $12,500 was invested at a 2.5% interest rate and $2,500 was invested at a 1.5% interest rate to achieve the total interest of $350 after one year.

Step-by-step explanation:

To solve how much money was invested at each interest rate, we'll use a system of equations. Let's denote the amount invested at 2.5% as x and the amount invested at 1.5% as y. The following equations represent the situation:

x + y = $15,000 (the total amount invested)

0.025x + 0.015y = $350 (the total interest earned in one year)

Now, to find the values of x and y, we solve the system of equations:

Multiply the second equation by 100 to get rid of the decimals: 2.5x + 1.5y = 35,000

Multiply the first equation by 1.5 to line up the y terms: 1.5x + 1.5y = 22,500

Subtract the second equation from the new first equation to eliminate y: 1x = 12,500

Therefore, x = $12,500, which is the amount invested at 2.5%

Substitute x back into the first equation to solve for y: 12,500 + y = 15,000

Therefore, y = $2,500, which is the amount invested at 1.5%

In summary, $12,500 was invested at 2.5% interest and $2,500 was invested at 1.5% interest.