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29 March, 08:55

an investor currently has 40,000 portfolio 40% of which is invested in bonds the investor wishes to add funds to the portfolio by purchasing bonds so that 52% of the entire portfolio will be invested in bonds. what value of bonds should the investor purchase?

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  1. 29 March, 11:57
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    The value of the bonds that the investor should purchase=$10,000

    Explanation:

    Step 1: Determine current value of portfolio and bonds

    Current value of portfolio=$40,000

    Current value of bonds=40% of 40,000

    Current value of bonds = (40/100) * 40,000=$16,000

    Step 2: Final value of bonds and portfolio

    Final value of bonds=current value of bonds+added value of bonds

    where;

    current value of bonds=16,000

    added value of bonds=X

    replacing;

    Final value of bonds=16,000+X

    Final value of portfolio=current value of portfolio+added value of bonds

    where;

    current value of portfolio=40,000

    added value of bonds=X

    replacing;

    Final value of portfolio=40,000+X

    Step 3: Solve for X

    Using the expression;

    Proportion of bonds = (final value of bonds/final value of portfolio) * 100

    where;

    proportion of bonds=52%

    final value of bonds=16,000+X

    final value of portfolio=40,000+X

    replacing;

    (52/100) = (16,000+X) / (40,000+X)

    0.52 = (16,000+X) / (40,000+X)

    0.52 (40,000+X) = 16,000+X

    20,800+0.52 X=16,000+X

    (X-0.52 X) = 20,800-16,000

    0.48 X=4,800

    X=4,800/0.48=10,000

    The value of the bonds that the investor should purchase=$10,000
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