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A total of $32,000 is invested in two municipal bonds that pay 4.25% and 6.25% simple interest. The investor wants an annual interest income of $1680 from the investments. What amount should be invested in the 4.25% bond?

Respuesta :

Answer:

$16000 invested in 4.25%  and 16000 invested in 6.25%

Step-by-step explanation:

Let x be the amount invested in 4.25%  and y be the amount invested in 6.25%

4.25%= 0.0425

6.25%= 0.0625

[tex]x+y= 32000[/tex]

subtract x from both sides

[tex]y= 32000-x[/tex]

total interest earned is 1680

[tex]0.0425x+0.0625y=1680[/tex]

[tex]0.0425x+0.0625(32000-x)=1680[/tex]

Now solve for x  and y

[tex]0.0425x+2000-0.0625x=1680[/tex]

subtract 2000 from both sides

[tex] -0.02x=1680-2000[/tex]

[tex] -0.02x=-320[/tex]

divide by -0.02 from both sides

x=16000

[tex]y= 32000-x[/tex]

[tex]y= 32000-16000=16000[/tex]