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
[tex]I_1=x \times \frac{5.75}{100}=\frac{5.75x}{100}.[/tex]
The remaining amount that can be invested in the 6.25% bond is 44000-x.
The annual simple interest for this amount is
[tex]I_2=(44000-x) \times \frac{6.25}{100}=\frac{6.25x}{100}.[/tex]
As the investor wants an annual interest income of $2,680, so
[tex]I_1 + I_2 = 2,680[/tex]
[tex]\Rightarrow \frac{5.75x}{100} + \frac{6.25x}{100} = 2680[/tex]
[tex]\Rightarrow \frac{5.75x+6.25x}{100}= 2680[/tex]
[tex]\Rightarrow \frac{12x}{100}= 2680[/tex]
[tex]\Rightarrow x= \frac {2680\times100}{12}[/tex]
[tex]\Rightarrow x=22333.33[/tex]
Hence, the amount to be invested at a rate of 5.75% is $22333.33.
