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.
Found 2 solutions by addingup, MathTherapy:
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! The last answer is obvious. The problem says that 1/4 of the portfolio must be invested in stocks.
There are two types of stocks:
Blue-Chip
Growth - Lets call these s. Therefore,
total in blue-chips = 125,000-s, where s is growth stocks
Now you have 500000-125,000 = 375,000 and 375,000/2 = 187,500 and this is the amount that is invested each in munis and CDs. I don't know why one says -s and the other +s
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
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.
As stated, amount invested in growth stocks = s
Let amount invested in CDs, bonds, and blue-chip stocks be C, B, and BC, respectively
As ¼ of portfolio needs to be invested in stocks, then s + BC = ¼ * 500,000
s + BC = 125,000____BC = 125,000 - s ------- eq (i)
Therefore, C + B = ¾ * 500,000____C + B = 375,000_____C = 375,000 - B ------- eq (ii)
As the CDs pay 3% annually, earnings form the CDs are: .03C
As the bonds pay 5% annually, earnings from the bonds are: .05B
As blue-chip stock should bring 8% annually, blue-chip stocks should bring .08BC
As growth stocks should return 10% annually, earnings from growth stocks = .1s
As annual returns need to be 5%, we get: .03C + .05B + .08BC + .1s = .05(500,000)
.03C + .05B + .08BC + .1s = 25,000 -------- eq (iii)
From eq (i), BC, or 
.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)
11,250 - .03B + .05B + 10,000 - .08s + .1s = 25,000
.02B + .02s = 3,750
.02(B + s) = .02(187,500) ------- Factoring out GCF, .02
B + s = 187,500
B, or 
C = 375,000 – (187,500 – s) ------- Substituting 187,500 – s for B in eq (ii)
C = 375,000 – 187,500 + s
C, or 
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