document.write( "Question 1034261: Consider an investor with a portfolio totaling $500000 that is invested in certificates of deposit, municipal bonds, blue-chip stocks, and growth or speculative stocks. The certificates of deposit pay 3% annually, and the municipal bonds pay 5% annually. Over a five-year period, the investor expects the blue-chip stocks to return 8% annually and the growth stocks to return 10% annually. The investor wants a combined annual return of 5% and also wants to have only one-fourth of the portfolio invested in stocks. How much is invested in each type of investment? The answers in the back of the book are 187500+s in certificates of deposit, 187500-s in municipal bonds, and 125000-s where s is in growth stocks. I'm not sure as how they got to these answers. \n" ); document.write( "
Algebra.Com's Answer #649031 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Consider an investor with a portfolio totaling $500000 that is invested in certificates of deposit, municipal bonds, blue-chip stocks, and growth or speculative stocks. The certificates of deposit pay 3% annually, and the municipal bonds pay 5% annually. Over a five-year period, the investor expects the blue-chip stocks to return 8% annually and the growth stocks to return 10% annually. The investor wants a combined annual return of 5% and also wants to have only one-fourth of the portfolio invested in stocks. How much is invested in each type of investment? The answers in the back of the book are 187500+s in certificates of deposit, 187500-s in municipal bonds, and 125000-s where s is in growth stocks. I'm not sure as how they got to these answers.
\n" ); document.write( "
As stated, amount invested in growth stocks = s
\n" );
document.write( "Let amount invested in CDs, bonds, and blue-chip stocks be C, B, and BC, respectively
\n" );
document.write( "As ¼ of portfolio needs to be invested in stocks, then s + BC = ¼ * 500,000
\n" );
document.write( "s + BC = 125,000____BC = 125,000 - s ------- eq (i)
\n" );
document.write( "Therefore, C + B = ¾ * 500,000____C + B = 375,000_____C = 375,000 - B ------- eq (ii)
\n" );
document.write( "As the CDs pay 3% annually, earnings form the CDs are: .03C
\n" );
document.write( "As the bonds pay 5% annually, earnings from the bonds are: .05B
\n" );
document.write( "As blue-chip stock should bring 8% annually, blue-chip stocks should bring .08BC
\n" );
document.write( "As growth stocks should return 10% annually, earnings from growth stocks = .1s
\n" );
document.write( "As annual returns need to be 5%, we get: .03C + .05B + .08BC  + .1s = .05(500,000)
\n" );
document.write( ".03C + .05B + .08BC + .1s = 25,000 -------- eq (iii)\r
\n" );
document.write( "\n" );
document.write( "From eq (i), BC, or    \r
\n" );
document.write( "\n" );
document.write( ".03(375,000 – B) + .05B + .08(125,000 – s) + .1s = 25,000 -------- Substituting 125,000 – s for BC, and 375,000 – B for C in eq (iii)
\n" );
document.write( "11,250 - .03B + .05B + 10,000 - .08s + .1s = 25,000
\n" );
document.write( ".02B + .02s = 3,750
\n" );
document.write( ".02(B + s) = .02(187,500) ------- Factoring out GCF, .02 
\n" );
document.write( "B + s = 187,500
\n" );
document.write( "B, or  \r
\n" );
document.write( "\n" );
document.write( "C = 375,000 – (187,500 – s) ------- Substituting 187,500 – s for B in eq (ii)
\n" );
document.write( "C = 375,000 – 187,500 + s
\n" );
document.write( "C, or  \n" );
document.write( "
\n" );