A mother wants to invest $9,000.00 for her son’s future education. She invents a portion of the money in a bank certificate of deposit (Cd account) which earns 4% and the remainder in a saving bond that earns 7%. If the total interest earned after one year is $540.00, how much money was invested in the CD account?
$X-Invested in CD.
$Y-Invested in bonds.
Eq1: 0.04X + 0.07Y = $540.
Eq2: X + Y = $9000.
Multiply Eq1 by 100 and Eq2 by -7:
4X + 7Y = 54000.
-7X -7Y = -63000.
Add the Eqs:
-3X = -9000.
X = $3000 Invested in a CD.
Jamal currently earns $20,000 a year in gross wages. On January 1, he is due to receive a 2% COLA. What will his gross income be after the COLA takes effect?
Let's assume the amount invested in the CD account is 'x'.
The amount invested in the saving bond will be the remainder, which is 9000 - x.
The interest earned from the CD account can be calculated as 0.04x (since the interest rate is 4%).
The interest earned from the saving bond can be calculated as 0.07(9000 - x) (since the interest rate is 7%).
We know that the total interest earned is $540.00. So we can set up the equation:
0.04x + 0.07(9000 - x) = 540
Now let's solve the equation step-by-step:
0.04x + 0.07(9000 - x) = 540
0.04x + 630 - 0.07x = 540
-0.03x + 630 = 540
-0.03x = 540 - 630
-0.03x = -90
x = (-90) / (-0.03)
x = 3000
Therefore, $3000.00 was invested in the CD account.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the amount of money invested in the CD account is "x" dollars.
According to the problem, the amount of money invested in the saving bond is the remainder of the $9,000.00, which is (9,000 - x) dollars.
The interest earned from the CD account can be calculated by multiplying the amount invested (x) by the interest rate (4%). Similarly, the interest earned from the saving bond can be calculated by multiplying the amount invested in the saving bond (9,000 - x) by the interest rate (7%).
Now, let's set up the equation:
0.04x + 0.07(9,000 - x) = 540
Simplifying the equation, we get:
0.04x + 630 - 0.07x = 540
Combining like terms, we have:
0.03x = 540 - 630
0.03x = -90
To solve for "x," divide both sides of the equation by 0.03:
x = -90 / 0.03
x = 3000
Therefore, the amount invested in the CD account is $3,000.00.