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Country Day's scholarship fund receives a gift of $ 125000. The money is invested in stocks, bonds, and CDs. CDs pay 3.75 % interest, bonds pay 3.5 % interest, and stocks pay 6.9 % interest. Country day invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 5155 , how much was invested in each vehicle?

User Guerric P
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1 Answer

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Let's represent the amounts invested in each vehicle as follows:

Let x be the amount invested in CDs (in dollars).

Then the amount invested in bonds would be (x + $25000) because Country Day invests $25000 more in bonds than in CDs.

And the remaining amount (gift - x - (x + $25000)) would be invested in stocks.

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

Income from CDs = x * 0.0375

Income from bonds = (x + $25000) * 0.035

Income from stocks = (gift - x - (x + $25000)) * 0.069

The total annual income is given as $5155:

Total Income = Income from CDs + Income from bonds + Income from stocks

So, we can write the equation:

$5155 = x * 0.0375 + (x + $25000) * 0.035 + (gift - x - (x + $25000)) * 0.069

Now, let's substitute the value of the gift, which is $125000:

$5155 = x * 0.0375 + (x + $25000) * 0.035 + ($125000 - x - (x + $25000)) * 0.069

Now, solve for x:

$5155 = 0.0375x + 0.035(x + $25000) + 0.069($125000 - 2x - $25000)

$5155 = 0.0375x + 0.035x + $1225 + $8610 - 0.138x - $1725

Combine the x terms:

$5155 = 0.035x + 0.0375x - 0.138x + $9885

Simplify and bring the x terms to one side:

$5155 = -0.0655x + $9885

Now, isolate x:

$5155 - $9885 = -0.0655x

-$4730 = -0.0655x

Divide both sides by -0.0655 to find x:

x ≈ $72327.48

Now, we can find the amount invested in bonds:

Amount in bonds = x + $25000

Amount in bonds = $72327.48 + $25000

Amount in bonds ≈ $97327.48

Finally, we can find the amount invested in stocks:

Amount in stocks = gift - x - (x + $25000)

Amount in stocks = $125000 - $72327.48 - ($72327.48 + $25000)

Amount in stocks ≈ $22672.52

So, approximately $72327.48 was invested in CDs, $97327.48 in bonds, and $22672.52 in stocks.

User TheRookierLearner
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