Question

Maricopa's Success scholarship fund receives a gift of $ 135000. The money is invested in stocks, bonds, and CDs. CDs pay 2.25 % interest, bonds pay 3.4 % interest, and stocks pay 6.1 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 5017.5 , how much was invested in each account?

Answer 1

CDs: $39,750

Bonds: $49,750

Stocks: $45,500

Explanation:

Let's denote the amount invested in CDs as "x" dollars. Since the investment in bonds is $10,000 more than in CDs, the amount invested in bonds would be "(x + 10000)" dollars. The rest of the money, which is the remaining amount after investing in CDs and bonds, would be invested in stocks and would be "(135000 - x - (x + 10000))" dollars.

Now, let's calculate the income from each investment:

Income from CDs = x * 0.0225 (2.25% interest)

Income from bonds = (x + 10000) * 0.034 (3.4% interest)

Income from stocks = (135000 - x - (x + 10000)) * 0.061 (6.1% interest)

The total annual income from all investments is given as

$5017.5:x * 0.0225 + (x + 10000) * 0.034 + (135000 - x - (x + 10000)) * 0.061 = 5017.5

Now, let's solve this equation to find the value of "x" and then calculate the amounts invested in each account:

0.0225x + 0.034(x + 10000) + 0.061(135000 - 2x - 10000) = 5017.5

Simplify the equation:

0.0225x + 0.034x + 340 + 0.061(135000 - 2x - 10000) = 5017.5

0.0565x + 0.061(125000 - 2x) = 5017.5

0.0565x + 7625 - 0.122x = 5017.5

-0.0655x = -2607.5

Now, solve for "x":

x = -2607.5 / -0.0655

x = 39750

Now that we have the value of "x," we can find the amounts invested in each account:

Amount invested in CDs = x = $39,750

Amount invested in bonds = x + $10,000 = $39,750 + $10,000 = $49,750

Amount invested in stocks = 135000 - x - (x + 10000) = 135000 - 39750 - (39750 + 10000) = $45,500

Therefore, the amounts invested in each account are as follows:

CDs: $39,750

Bonds: $49,750

Stocks: $45,500