$16,687 is Invested,part at 12% And the rest at 8% if the interest earned from the amount invested at 12% exceeds the interest earned from the amount invested at 8% by $1903.24 how much is invested at each rate
if $x is at 12%, the rest (16687-x) is at 8%. So,
0.12x = 0.08(16687-x) + 1903.24
Let's assume the amount invested at 12% is X. Therefore, the amount invested at 8% would be (16,687 - X), as the total amount invested is $16,687.
The interest earned from the amount invested at 12% can be calculated as (X * 0.12), and the interest earned from the amount invested at 8% is ((16,687 - X) * 0.08).
According to the given information, the interest earned from the amount invested at 12% exceeds the interest earned from the amount invested at 8% by $1903.24. We can express this as:
(X * 0.12) - ((16,687 - X) * 0.08) = 1903.24
Now let's solve the equation step by step:
0.12X - 0.08(16,687 - X) = 1903.24
0.12X - 0.08 * 16,687 + 0.08X = 1903.24
0.12X - 1334.96 + 0.08X = 1903.24
0.2X = 1903.24 + 1334.96
0.2X = 3238.2
X = 3238.2 / 0.2
X = 16,191
Therefore, $16,191 is invested at 12% and the remaining amount, $16,687 - $16,191 = $496, is invested at 8%.
To solve this problem, let's assume that the amount invested at 12% is x, and the amount invested at 8% is y.
We know that the total amount invested is $16,687, so we can write the equation:
x + y = 16,687 ... Equation 1
We are also given that the interest earned from the amount invested at 12% exceeds the interest earned from the amount invested at 8% by $1,903.24. The interest earned can be calculated using the formula:
Interest = Principal * Rate
Therefore, the interest earned from the amount invested at 12% is (0.12 * x), and the interest earned from the amount invested at 8% is (0.08 * y). We can now write the second equation:
0.12x - 0.08y = 1,903.24 ... Equation 2
Now we have a system of two equations with two variables. We can solve them simultaneously to find the values of x and y.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.
Multiplying Equation 1 by 0.08, we get:
0.08x + 0.08y = 1,335.76 ... Equation 3
Now, subtract Equation 3 from Equation 2:
0.12x - 0.08x - 0.08y - 0.08y = 1,903.24 - 1,335.76
0.04x = 567.48
Divide both sides of the equation by 0.04:
x = 567.48 / 0.04
x = 14,187
Substituting the value of x into Equation 1, we can find the value of y:
14,187 + y = 16,687
y = 16,687 - 14,187
y = 2,500
Therefore, $14,187 is invested at 12% and $2,500 is invested at 8%.