A mother wants to invest 8,000 dollars into her child's college fund. She invests a portion of the money into a CD account which earns 4% interest, and the remainder into a savings bond which earns 7% interest. If the total interest earned after one year is $480.00, how much money was invested in the CD account?
amount into lower rate account --- x
amount into higher rate account --- 8000-x
.04x + .07(8000-x) = 480
4x + 7(8000-x) = 48000
4x + 56000 - 7x = 48000
-3x = -8000
x = 8000/3 = 2666.67
amount into CD = $2666.67
Well, investing in a CD account can be pretty a-maize-ing! Let's solve this puzzle together, shall we?
Let's call the amount invested in the CD account "x" (in dollars). Since the mother invested a total of $8,000, the amount invested in the savings bond would be $8,000 - x.
Now, the CD account earns 4% interest, and the savings bond earns 7% interest. So, the interest earned on the CD account would be 0.04x, and the interest earned on the savings bond would be 0.07(8,000 - x).
We know that the total interest earned after one year is $480.00, so we can set up an equation:
0.04x + 0.07(8,000 - x) = 480
Now, let's put on our mathematical spectacles and solve this equation:
0.04x + 0.07(8,000 - x) = 480
0.04x + 560 - 0.07x = 480
0.03x + 560 = 480
0.03x = 480 - 560
0.03x = -80
x = -80 / 0.03
x ≈ -2,666.67
Oh no! It seems like we've hit a clown-undrum! The negative amount doesn't make sense in this context, so there might be a misstep in the calculations or information provided. Please double-check and re-enter the values, and I'll be happy to help you with the correct answer!
Let's assume the amount invested in the CD account is x dollars, and the amount invested in the savings bond is (8000 - x) dollars.
The interest earned on the CD account is 4% of x dollars, which can be expressed as 0.04x.
The interest earned on the savings bond is 7% of (8000 - x) dollars, which can be expressed as 0.07(8000 - x).
The total interest earned is given as $480.00, so we can set up the equation:
0.04x + 0.07(8000 - x) = 480
Now, let's solve the equation step-by-step:
0.04x + 0.07(8000 - x) = 480
0.04x + 560 - 0.07x = 480
-0.03x + 560 = 480
-0.03x = 480 - 560
-0.03x = -80
To isolate x, we divide both sides of the equation by -0.03:
(-0.03x) / -0.03 = (-80) / -0.03
x = 2666.67
Therefore, the mother invested approximately $2666.67 in the CD account.
To determine how much money was invested in the CD account, let's use algebraic expressions. Let x represent the amount of money invested in the CD account.
Given:
Total investment: $8,000
Interest earned from the CD account: 4%
Interest earned from the savings bond: 7%
Total interest earned after one year: $480
To solve the problem, we can set up an equation using the information provided:
(4% of x) + (7% of (8000 - x)) = $480
To solve, let's convert the percentages to decimal form:
0.04x + 0.07(8000 - x) = 480
Now, we can simplify the equation:
0.04x + 560 - 0.07x = 480
Combining like terms, we have:
-0.03x + 560 = 480
Subtracting 560 from both sides of the equation:
-0.03x = -80
Now, let's solve for x by dividing both sides of the equation by -0.03:
x = (-80) / (-0.03)
x ≈ 2666.67
Therefore, approximately $2,666.67 was invested in the CD account.