document.write( "Question 1186746: A person has $50,000 to invest. As the​ person's financial​ consultant, you recommend that the money be invested in Treasury bills that yield 4% Treasury bonds that yield 8% and corporate bonds that yield  12% The person wants to have an annual income of $3920 and the amount invested in corporate bonds must be half that invested in Treasury bills. Find the amount in each investment. \n" ); document.write( "
Algebra.Com's Answer #817710 by ikleyn(52847)\"\" \"About 
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\n" ); document.write( "A person has $50,000 to invest. As the​ person's financial​ consultant, you recommend that
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\n" ); document.write( "The person wants to have an annual income of $3920 and the amount invested in corporate bonds
\n" ); document.write( "must be half that invested in Treasury bills. Find the amount in each investment.
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document.write( "Let x be the amount invested in corporate bonds (12%), in dollars.\r\n" );
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document.write( "Then the amount invested in Treasury bills (4%) is twice of it, i.e. 2x dollars,\r\n" );
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document.write( "and the amount invested in Treasury bonds (8%) is the rest  (50000-x-2x) = (50000-3x)  dollars.\r\n" );
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document.write( "At this point, you can write the total annual interest equation\r\n" );
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document.write( "    0.12x + 0.04*(2x) + 0.08*(50000-3x) = 3920.\r\n" );
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document.write( "The setup is completed.  To solve the equation, simply it step by step\r\n" );
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document.write( "    0.12x + 0.08x + 0.08*50000 - 0.24x = 3920\r\n" );
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document.write( "    0.12x + 0.08x - 0.24x = 3920 - 0.08*50000\r\n" );
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document.write( "           - 0.04x        = -80\r\n" );
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document.write( "                 x        = -80/(-0.04) = 80/0.04 = 8000/4 = 2000.\r\n" );
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document.write( "Thus the amount invested in corporate bonds is  x = 2000  dollars;\r\n" );
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document.write( "                invested in Treasury  bills is  2x = 2*2000 = 4000  dollars,\r\n" );
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document.write( "           and  invested in Treasury  bonds is the rest 50000 - 2000 - 4000 = 44000  dollars.\r\n" );
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document.write( "CHECK.  0.12*2000 + 0.04*4000 + 0.08*44000 = 3920  dollars, the total annual interest.    ! Correct !\r\n" );
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