QuestionA mother invests \$8,000 in a CD at 4% and a bond at 7%, earning \$480 in interest. How much is in the CD?

Studdy Solution

STEP 1

Assumptions1. The total amount to be invested is $8,000. The interest rate for the CD account is4%<br />3. The interest rate for the savings bond is7%<br />4. The total interest earned after one year is$ 4805. The interest is calculated as a one-time payment, not monthly compounding

STEP 2

Let's denote the amount invested in the CD account as $x$ and the amount invested in the savings bond as $8000 - x$ .

STEP 3

The total interest earned from both investments is the sum of the interest earned from the CD account and the savings bond. We can express this as an equation $Total\, interest = Interest\, from\, CD\, account + Interest\, from\, savings\, bond$

STEP 4

We can calculate the interest from each account by multiplying the amount invested by the interest rate. Substituting these expressions into our equation gives $480 =0.04x +0.07(8000 - x)$

STEP 5

Now, we can simplify this equation. First, distribute the0.07 to both terms in the parentheses $480 =0.04x +560 -0.07x$

STEP 6

Next, combine like terms $480 = -0.03x +560$

STEP 7

To isolate $x$ , we can subtract560 from both sides of the equation $-80 = -0.03x$

STEP 8

Finally, divide both sides by -0.03 to solve for $x$ $x = \frac{-80}{-0.03}$

STEP 9

Calculate the value of $x$ .
$x = \frac{-80}{-.03} = \$2,666.67$ The mother invested $2,666.67 in the CD account.

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