Expert: Bobby Soltani - 8/13/2009

Question
QUESTION: Hello:

How can I determine the answers for the following?

An investor wants to divide $1000.00 into two amounts, $800.00 and $200.00. At what percentages will these two accounts need to earn in order for his total return to be 4.4% or $44/$1000?

$800.00 X ?% + $200.00 X ?% = $44.00

Answers: 5% and 2%
$800 X 5% = $40.00 + $200 + 2% = $4.00 = $44.00

If possible, can you use a non-algebra calculation?

I thank you for your reply.

ANSWER: Hi Kenneth,

There are actually several percentages that will earn a total of 4.4%.  You set up the equation correctly.

800*P1 + 200*P2 = 4400   (note: I used 4400 instead of 44 to get P1 and P2 as a percentage)

P2 = -4P1 + 22

So, for any P1, P2 is equal to -4P1 + 22 percent.

Let me know if you have any questions.

Bobby

---------- FOLLOW-UP ----------

QUESTION: Hello Bobby:

I want to thank you for your reply.

However, I need more detailed information. I do not understand how you got 4400.  What are P1 and P2, and what do they represent?

Can you find a solution even though there are several percentages that will earn a total of 4.4%?

I thank you for your follow-up reply.

ANSWER: P1 and P2 represent the interest rates (or percentages).  Since 4% is equal to 0.04, I multiplied both sides of the equation by 100 to get P1 and P2 in terms of a percentage (e.g., 4 percent instead of 0.04).  Sorry for any confusion that may have caused.  You can leave 44 as it is, then the relationship will be

P2 = -.04P1   0.22

I hope that helps.


---------- FOLLOW-UP ----------

QUESTION: Hello:

I understand the solution except the final result.

Divide the equation 800*P1 + 200*P2 = 400 by 100.
This equals 8*P1 +2*P2 = 44.

Divide 8*P1 + 2*P2 = 44 by 2.
This equals 4*P1 +P2 = 22%.

Now subtract 4*P1  from both sides and this equals the following:
P2 = -4*P1 + 22%

1. How does 22 become 22%?

2. What do I do with P2 = -4*P1 + 22%?

Can you explain fully? I thank you for your reply.  

Answer
Hi,
Percentage means "per 100", so 50% means 50 per 100, or simply 50/100.  If you divide 50 by 100 you get 0.5 (a decimal number). So, to convert from percentage to decimal: divide by 100 (and remove the "%" sign). The easiest way to divide by 100 is to move the decimal point 2 places to the left.  Similarly, you can multiply a decimal number by 100 to get the value in a percentage form.  For example 0.30 is the same as 30%, which is 0.30*100.

Let's work this equation out in terms of decimal number (e.g., P1 and P2 will be between 0 and 1)

800*P1 + 200*P2 = 44

divide both sides by 100

8P1 + 2P2 = 0.44

divide both sides by 2

4P1 + P2 = 0.22

Now any positive numbers P1 and P2 that satisfy this equation will yeild 4.4% or 0.044 return.

Bobby