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### Return on Investments

```
Date: 10/14/98 at 23:12:42
From: jolene quinn
Subject: ROI percentage

What is the formula for calculating the return on investments (ROI%)?
I can't seem to remember it, and I would appreciate it if you could
help me out.
```

```
Date: 10/22/98 at 01:12:32
From: Doctor Andrewg
Subject: Re: ROI percentage

Hi Jolene!

I'm assuming here that you are talking out the return on investment
(ROI) where you invest your money and then at a fixed time later on
get some money back. You can also have an ROI for more complicated
situations where you invest some money to start with and then have
various expenses and revenues at certain points of time. If you do
mean the latter then just let me know and I'll explain that as well.

First of all we need to define what we mean by return on investment.

If we invest a sum of money, into a bank account, then we (usually)
earn interest from the bank. Let's say that the interest rate is 10
percent and we invest \$100. If we ignore taxes and bank fees (if only
we really could do this), then at the end of the year we will have \$110
(\$100 + 10% of \$100, or \$100 * 1.1) in our account.

Our return on investment for that year is:

(the amount we have at the end) - (the amount we had at the start)
------------------------------------------------------------------
(the amount we had at the start)

or:

(the extra amount we have)
--------------------------------
(the amount we had at the start)

In this case this equals:

(\$110-\$100)   \$10
----------- = ---- = 0.1
\$100      \$100

And we know that 0.1 equals 10%, right? So the return on investment is
the same as the interest rate.

If we instead invest money in a business or a project, the same thing
happens. Say we invest \$5000 in an ice cream stand (equipment,
uniforms, etc.) and make \$500 profit in our first month. The \$500 is
the amount we earned in selling ice cream less the cost of making those
ice creams (say, \$700 - \$200 = \$500, but it doesn't matter when we
calculate ROI).

Then our return on investment for that month is:

(the amount we have at the end) - (the amount we had at the start)
------------------------------------------------------------------
(the amount we had at the start)

(the ice cream stand + our profit)
= -----------------------------------------------
(the amount we invested in the ice cream stand)

[note that we still have our ice cream stand at the end]

(\$5000+\$500) - (\$5000)
= ----------------------
(\$5000)

(the extra amount we have (profit))
[note this equals  -----------------------------------------]
(the amount we had invested in the stand)

\$500
= -----
\$5000

= 0.1,  which is 10% again.

So if we had invested our \$5000 in the bank and earned 10% interest we
would have had the same amount at the end of a year, \$5500. This time
we made a 10% ROI, but in only one month instead of a whole year.

Are ROIs always positive?  What would happen if instead of earning \$500
profit on our ice cream stand, we lost \$500? Try plugging the numbers
in and see what answer you get out.

If you have any other questions please ask me; I'll be only too happy
to try to explain.

- Doctor AndrewG, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Interest

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