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Advanced Math/Investment Profit - Percentage

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Expert: - 7/10/2009


Question
QUESTION: Hello:

An investor invest $100.00 for one year at simple interest.
At the end of one year his investment earns $50.00. The management company deducted a 2.5% management fee. What was the investor's percentage return on his investment?

Is it ($50.00 - 2.5% divided by $100.00 divided by 1/100 = 48.75%? or is it $150.00 - 2.5%) - $100.00 divided by 100, or neither?

I thank you for your reply.


ANSWER: Is the 2.5% fee only on the $50.00 that he made?

In that case, 2.5% is the same as 2.5/100 = 25/1000.

If we take 50*25/1000, the answer would be 1250/1000,
or $1.25.

Note that when the 2.5% is applied to $100, $2.50 is gotten.

Since $50 is half of $100, it can be seen that $1.25
is half of $2.50.


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

QUESTION: Hello:

I want to thank you for the reply.

The fee is applied to the entire amount of $150.00. I think that it would be $150.00 minus (2.5% of $150.00). The investor would get what remains, $146.25.  So would it be
($146.25 - $100)/$100 = $46.25/$100.00 = 0.4625 or 46.25% (?)

The $100.00 should be subtracted from what remains to get his profit amount.

I thank you for your follow-up reply.

Answer
Yes, the profit is $50.

If the fee were charged on the original $100, it would be $2.50.

If the fee were charage on the entire $150, it would be $3.75.

If the fee were charged on the gain of $50, is would be $1.25.


Note that 2.5% of $100 is seen to be 0.025($100) = $2.50.

Since $50 is halfe of $100, the interest on 50 would be half of the interest on $100.  That is, (1/2)($2.5) = $1.25.

Since $150 is $100 + $50, the fee would be $2.50 + $1.25 = $3.75.
If could also be done directly, $150*0.025 = $3.75.

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