Question

Katie invested a total of $5000, part at 2% simple interest and part at 3% simple interest. At the end of 1 year, the investments had earned $126 interest. How much was invested at each rate? Katie investeds at a rate of 2% and $ at a rate of 3%

Answer 1

Katie invested $ 2400 at 2% and $ 2600 at 3% simple interest. By setting up equations representing the total amount invested and the total interest earned, we solved for the amounts invested at each interest rate.

Step-by-step explanation:

To solve the question of how much was invested at each simple interest rate by Katie, we need to set up two equations based on the total amount invested and the total interest earned. Let's denote the amount invested at 2% as $x and the amount at 3% as $(5000-x), since the total invested is $ 5000.

Now, we write our two equations

1. The sum of the two investments equals $ 5000: $x + $(5000 - x) = $ 5000.
2. The total interest earned from both investments after one year is $ 126: 0.02 $x + 0.03 $(5000 - x) = $ 126

Solving these equations, we first simplify the second equation:

0.02x + 0.03 $(5000) - 0.03x = $ 126

Combine like terms to find the interest amount invested at each rate:

-0.01x + 0.03 $(5000) = $ 126

-0.01x = $ 126 - 0.03 $5,000

-0.01x = $ 126 - $ 150

-0.01x = -$ 24

x = $ 2400 (amount at 2%) and 5000-x = $ 2600 (amount at 3%)

Therefore, Katie invested $ 2400 at 2% and $ 2600 at 3% simple interest.