Eva invested a certain amount of money at 12% interest and $1500 more than that amount at 13%. Her total yearly interest was $800. How much did she invest at each rate?
.12x + .13(x+1500) = 800
x = 2420
so, $2420 at 12% and $3920 at 13%
To find out how much Eva invested at each interest rate, let's assume she invested x dollars at 12% interest.
According to the given information, she also invested $1500 more than that amount at 13% interest. So her investment at 13% interest would be (x + $1500).
The amount of interest earned on an investment can be calculated using the formula:
Interest = (Principal * Rate * Time)
For the investment at 12% interest:
Interest1 = (x * 0.12 * 1) (as the time is given as 1 year)
For the investment at 13% interest:
Interest2 = ((x + $1500) * 0.13 * 1) (again, the time is given as 1 year)
According to the given information, the total interest earned from both investments is $800:
Interest1 + Interest2 = $800
Therefore, we can write the equation as:
0.12x + 0.13(x + $1500) = $800
To solve this equation, we can simplify it by distributing:
0.12x + 0.13x + 0.13 * $1500 = $800
0.12x + 0.13x + $195 = $800
Combining like terms:
0.25x + $195 = $800
Now, let's isolate the variable x by subtracting $195 from both sides of the equation:
0.25x = $800 - $195
0.25x = $605
Finally, divide both sides of the equation by 0.25 to solve for x:
x = $605 / 0.25
x ≈ $2420
Therefore, Eva invested approximately $2420 at 12% interest.
To find how much she invested at 13% interest, we can substitute the value of x into the equation:
Investment at 13% = x + $1500
= $2420 + $1500
= $3920
Therefore, Eva invested approximately $2420 at 12% interest and $3920 at 13% interest.