Katie invested a total of $6000
,
part at 3
%
simple interest and part at 4
%
simple interest. At the end of 1 year, the investments had earned $214
interest. How much was invested at each rate?
Good subject
Let's assume Katie invested x dollars at 3% simple interest.
This means she invested (6000 - x) dollars at 4% simple interest.
The interest earned from the 3% investment can be calculated as:
Interest_3% = x * 0.03
The interest earned from the 4% investment can be calculated as:
Interest_4% = (6000 - x) * 0.04
The total interest earned is given as $214, so we can write the equation:
Interest_3% + Interest_4% = $214
Substituting the equations for the interest earned:
x * 0.03 + (6000 - x) * 0.04 = $214
Simplifying the equation:
0.03x + 240 - 0.04x = $214
Combining like terms:
-0.01x = $214 - $240
Simplifying further:
-0.01x = -$26
To solve for x, we divide both sides of the equation by -0.01:
x = -$26 / -0.01
x = $2600
Therefore, Katie invested $2600 at 3% simple interest and (6000 - 2600) = $3400 at 4% simple interest.
To solve this problem, let's assume that Katie invested some amount, x, at 3% interest, and the remaining amount, 6000 - x, at 4% interest.
The interest earned from the investment at 3% interest is given by the formula: interest = principal * rate * time. So, the interest earned at 3% interest is 0.03x.
Similarly, the interest earned from the investment at 4% interest is given by the formula: interest = principal * rate * time. So, the interest earned at 4% interest is 0.04(6000 - x).
We are given that at the end of 1 year, the investments had earned $214 in interest. So, we can write the equation:
0.03x + 0.04(6000 - x) = 214
Now, let's solve this equation to find the value of x:
0.03x + 0.04(6000 - x) = 214
0.03x + 240 - 0.04x = 214
-0.01x = -26
x = -26 / -0.01
x = 2600
Now that we have found x, we can determine the amount invested at each rate:
Amount invested at 3% interest = $2600
Amount invested at 4% interest = $6000 - $2600 = $3400
So, Katie invested $2600 at 3% interest and $3400 at 4% interest.
amount invested at 3% --- x
amount invested at 4% --- 6000-x
.03x + .04(6000-x) = 214
continue...