Answer:
$16,000
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
Let investment 1 be the bond that pays 5.75% simple interest.
Let investment 2 be the bond that pays 7.25% simple interest.
Given:
Create two equations for the interest from both investments.
Interest from Investment 1
[tex]\implies \sf I_1=P_1 \cdot 0.0575 \cdot 1[/tex]
[tex]\implies \sf I_1=0.0575\:P_1[/tex]
Interest from Investment 2
[tex]\implies \sf I_2=P_2 \cdot 0.0725 \cdot 1[/tex]
[tex]\implies \sf I_2=(28000-P_1)0.0725[/tex]
[tex]\implies \sf I_2=2030-0.0725\:P_1[/tex]
Given that the sum of the interest from both investments is $1,790:
[tex]\implies \sf I_1+I_2=1790[/tex]
[tex]\implies \sf 0.0575\:P_1+2030-0.0725\:P_1=1790[/tex]
[tex]\implies \sf -0.015\:P_1=-240[/tex]
[tex]\implies \sf P_1=16000[/tex]
Therefore, $16,000 should be invested in the 5.75% bond.
Check:
[tex]\implies \sf I_1=16000 \cdot 0.0575 \cdot 1 = 920[/tex]
[tex]\implies \sf I_2=12000 \cdot 0.0725 \cdot 1 = 870[/tex]
[tex]\implies \sf I_1+I_2=920+870=1790[/tex]