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

Guest Mar 28, 2017

#3**+2 **

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

Melody
Mar 28, 2017

#3**+2 **

Best Answer

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

Melody
Mar 28, 2017

#4**+2 **

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 ]

CPhill
Mar 28, 2017