Question

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?

Answer 1

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

Step-by-step 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