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Ebony but a four year treasury note that pay the equivalent of 3.8% simple interest. She invested $3000 more in a 9 year bond earning 4.6% than she did in the treasury note. If the total amount of interest from these investments was $5204 determine the amount of principle of each investment. Please help!

Respuesta :

Cricetus

Treasury bond's invested amount is "$7000" and Bond's invested amount is "$10000",

Let,

  • The amount invested in treasury note will be = x
  • The amount invested in bond will be = (x + 3000)

then,

→ [tex]\frac{x\times 4\times 3.8}{100} +\frac{(3000+x)\times 9\times 4.6}{100}=5204[/tex]

→       [tex]\frac{15.2x}{100}+\frac{(3000+x)\times 41.4}{100} =5204[/tex]

→         [tex]\frac{15.2x}{100} +\frac{124200+41.4x}{100} =5204[/tex]

→            [tex]\frac{15.2 x+124200+41.4x}{100} = 5204[/tex]

→               [tex]56.6x+124200=520400[/tex]

→                               [tex]56.6x=520400-124200[/tex]

→                               [tex]56.6x=396200[/tex]

→                                      [tex]x = \frac{396200}{56.6}[/tex]

→                                         [tex]= 7000[/tex]

Amount invested in bond will be:

= [tex]x+3000[/tex]

= [tex]7000+3000[/tex]

= [tex]10000[/tex]    

Thus the above is the correct answer.

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