Answer:
$22333.33
Step-by-step explanation:
The total amount to be invested is $44,000.
Let x be the amount that can be invested in the 5.75% bond.
So, the annual simple interest for this amount is
![I_1=x \times \frac{5.75}{100}=\frac{5.75x}{100}.](https://tex.z-dn.net/?f=I_1%3Dx%20%5Ctimes%20%5Cfrac%7B5.75%7D%7B100%7D%3D%5Cfrac%7B5.75x%7D%7B100%7D.)
The remaining amount that can be invested in the 6.25% bond is 44000-x.
The annual simple interest for this amount is
![I_2=(44000-x) \times \frac{6.25}{100}=\frac{6.25x}{100}.](https://tex.z-dn.net/?f=I_2%3D%2844000-x%29%20%5Ctimes%20%5Cfrac%7B6.25%7D%7B100%7D%3D%5Cfrac%7B6.25x%7D%7B100%7D.)
As the investor wants an annual interest income of $2,680, so
![I_1 + I_2 = 2,680](https://tex.z-dn.net/?f=I_1%20%2B%20I_2%20%3D%202%2C680)
![\Rightarrow \frac{5.75x}{100} + \frac{6.25x}{100} = 2680](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B5.75x%7D%7B100%7D%20%2B%20%5Cfrac%7B6.25x%7D%7B100%7D%20%3D%202680)
![\Rightarrow \frac{5.75x+6.25x}{100}= 2680](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B5.75x%2B6.25x%7D%7B100%7D%3D%202680)
![\Rightarrow \frac{12x}{100}= 2680](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B12x%7D%7B100%7D%3D%202680)
![\Rightarrow x= \frac {2680\times100}{12}](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%20%5Cfrac%20%7B2680%5Ctimes100%7D%7B12%7D)
![\Rightarrow x=22333.33](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D22333.33)
Hence, the amount to be invested at a rate of 5.75% is $22333.33.