Answer:
The value of the bonds that the investor should purchase=$10,000
Explanation:
<em>Step 1: Determine current value of portfolio and bonds</em>
Current value of portfolio=$40,000
Current value of bonds=40% of 40,000
Current value of bonds=(40/100)×40,000=$16,000
<em>Step 2: Final value of bonds and portfolio</em>
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
<em>Step 3: Solve for X</em>
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
