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.