$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 $1093.24, How much is invested at each rate
Let's assume the amount invested at 12% is x.
Therefore, the amount invested at 8% is (16687 - x), since the total investment is $16,687.
The interest earned from the amount invested at 12% is given by (x * 0.12).
The interest earned from the amount invested at 8% is given by ((16687 - 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 $1093.24.
So, we can set up the following equation:
(x * 0.12) - ((16687 - x) * 0.08) = 1093.24
Simplifying the equation:
0.12x - 0.08(16687 - x) = 1093.24
0.12x - 0.08 * 16687 + 0.08x = 1093.24
0.12x - 1334.96 + 0.08x = 1093.24
0.20x - 1334.96 = 1093.24
0.20x = 1093.24 + 1334.96
0.20x = 2428.20
x = 2428.20 / 0.20
x ≈ 12141
So, approximately $12,141 is invested at 12%, and the remaining amount (16687 - 12141) ≈ $4,546 is invested at 8%.
To solve this problem, we can use a system of equations.
Let's assume that x dollars are invested at 12% and the remaining amount, which is ($16,687 - x), is invested at 8%.
We know that the interest earned from the amount invested at 12% exceeds the interest earned from the amount invested at 8% by $1093.24.
So, we can set up the following equation based on the interest formula:
0.12x - 0.08($16,687 - x) = $1093.24
Next, let's solve this equation step by step:
0.12x - 0.08($16,687) + 0.08x = $1093.24
0.12x - $1334.96 + 0.08x = $1093.24
Combine the x terms:
0.20x - $1334.96 = $1093.24
Now, isolate the x term:
0.20x = $1093.24 + $1334.96
0.20x = $2428.20
Divide both sides by 0.20 to solve for x:
x = $2428.20 / 0.20
x = $12,141
So, $12,141 is invested at 12% and the remaining amount ($16,687 - $12,141 = $4,546) is invested at 8%.
Therefore, $12,141 is invested at 12% and $4,546 is invested at 8%.