An investment adviser invested $14,000 in two accounts. One investment earned 4% annual simple interest, and the other investment earned 2.5% annual simple interest. The amount of interest earned for 1 year was $458. How much was invested in each account?
Invested $X @ 4%.
Invested $(14,000-X) @ 2.5%.
0.04X + 0.025(14000-X) = $458.
Solve for X.
Let's represent the amount invested in the account earning 4% annual interest as "x" (in dollars).
Then, the amount invested in the account earning 2.5% annual interest would be "14000 - x" (in dollars).
Now, let's calculate the interest earned from each investment:
Interest from the 4% account = (4/100) * x = 0.04x dollars
Interest from the 2.5% account = (2.5/100) * (14000 - x) = 0.025(14000 - x) dollars
Since we know that the total interest earned is $458, we can set up the following equation:
0.04x + 0.025(14000 - x) = 458
Now, let's solve for x:
0.04x + 0.025(14000 - x) = 458
0.04x + 350 - 0.025x = 458
0.015x + 350 = 458
0.015x = 458 - 350
0.015x = 108
x = 108 / 0.015
x = 7200
Therefore, $7200 was invested in the account earning 4% annual interest, and $14000 - $7200 = $6800 was invested in the account earning 2.5% annual interest.
To solve this problem, we can set up a system of equations. Let's denote the amount invested in the 4% interest account as 'x', and the amount invested in the 2.5% interest account as 'y'.
Since the investment in the 4% interest account earns simple interest, we can calculate the interest earned from that investment using the formula: Interest = Principal * Rate * Time. In this case, the interest earned from the 4% investment is given as $x * 4% = 0.04x.
Similarly, the interest earned from the 2.5% investment is $y * 2.5% = 0.025y.
According to the problem, the total interest earned for one year is $458. So, we can set up the equation: 0.04x + 0.025y = $458.
We also know that the total amount invested is $14,000, so we can set up another equation: x + y = $14,000.
Now we have a system of two equations:
0.04x + 0.025y = $458
x + y = $14,000
To solve this system, we can use the method of substitution or elimination. I'll use the elimination method here.
Let's multiply the second equation by 0.025 to make the coefficients of 'y' in both equations the same:
0.025x + 0.025y = $350
Now, we subtract the modified second equation from the first equation:
(0.04x + 0.025y) - (0.025x + 0.025y) = $458 - $350
This simplifies to:
0.015x = $108
Dividing both sides of the equation by 0.015 gives us:
x = $108 / 0.015
Calculating this, we find that x = $7200.
Now, we can substitute this value of x into the second equation to find the value of y:
$7200 + y = $14,000
Subtracting $7200 from both sides gives us:
y = $14,000 - $7200
So, y = $6800.
Therefore, $7200 was invested in the 4% interest account, and $6800 was invested in the 2.5% interest account.