Hi,
I have a question that needs to be answered as soon as I can.
The question is:
Suppose 40% of the dollar value of a stock portfolio consists of a high risk component, and 30% of the dollar value is in a safe category of investments. If $20,000 is added to portfolio in the high risk component, the safe component represnts 20% of the value of the portfolio. What is the new total dollar value of the portfolio?
I just don't seem to quite understand what is actually happening in the scenario of the question.
Any help and solutions would be greatly appreciated.
Thanks alot!
James
+118667 Hi James,
Yes this is an unusual question.
Let the original amount of investment be x dollars
The new amount will be x+ 20000 dollars
30% of the original is equal to 20% of the new amount.
\(0.3*x = 0.2*(x+20000)\\ 0.3x =0.2 x+4000\\ 0.1x=4000\\ x=40000 \)
So the new total value is 40000+20000 = $60 000
check:
0.3*40000=12000
0.2*60000=12000
+118667 Hi James,
Yes this is an unusual question.
Let the original amount of investment be x dollars
The new amount will be x+ 20000 dollars
30% of the original is equal to 20% of the new amount.
\(0.3*x = 0.2*(x+20000)\\ 0.3x =0.2 x+4000\\ 0.1x=4000\\ x=40000 \)
So the new total value is 40000+20000 = $60 000
check:
0.3*40000=12000
0.2*60000=12000
+129847 Call A the original amount in the portfolio......when $20000 is added to the high-risk component [ without adding anything to the safe component ], the new value of the portfolio = A + 20000
So, with reference to the safe component.....20% of the new amount = 30% of the original amount
.20(A + 20000) = .30A
.20A + 4000 = .30A
.10A = 4000
A = 40000 .....this is the original value of the portfolio
A + 20000 = 40000 + 20000 = $60000 = new value of the portfolio
[ Melody is correct....this is a good "thinking" problem ]
