Expert: Josh - 12/18/2005

Question
Hello:

I want to thank you for the reply.

1. Is this a weighted average if the principles are equal? The average would be ($15,000/$30,000 X 0.05) + ($15,000/$30,000 X 0.02) = 0.025 + 0.010 = 0.035 or 3.5%.

2. Why is it regarded as an average since no division is used in either of these calculations?

I thank you for your follow-up reply.
-------------------------
Followup To
Question -
Hello:

If $30,000 is invested at simple annual interest as $20,000 earning 5% and $10,000 earning 2%, the amount from both of these is $1,000 + $200 = $1,200. However, the $30,000 earned 4%, $1,200/$30,000 = 4%. Why isn't the percentage of 4% the average of (5% + 2%)/2 = 3.5% instead of 4%?


I thank you for your reply.
Answer -
You should consider the "weighted" average instead, because the principles are unequal. i.e., you started with $20,000 and $10,000, respectively.

Consider the weighted average:
(20,000/30,000)*0.05+(10,000/30,000)*0.02
=(2/3)*0.05+(1/3)*0.02
=0.04 (this is 4%)


Answer
1. Weighted average is a more general concept. The average you are used to seeing is a specific instance of a weighted average, where the weights are equal.

2. ($15,000/$30,000) is effectively a division.
($15,000/$30,000)*0.05+($15,000/$30,000)*0.02
is equivalent to (1/2)*0.05+(1/2)*0.02 = [0.05+0.02]/2.

Hope this completes the picture:)