Financial Mathematics: How to Find the Percentage Change

• Image by Gerd Altmann from Pixabay

In this article, I'm going to be demonstrating how to calculate a percentage change. Since many of you reading this will be dealing with crypto cash, you may find this post useful.

So, let's say for example your one Bitcoin is worth £8,200. Let's then say after a couple of days, its value rose to £8,400. What was the percentage change?

Well, you had a starting value of £8,200. Let's call this (x). You ended up with your starting value (x) plus the percentage change (p) multiplied by your starting value (p*x). We'll call this final value (y).

x = starting value

p = percentage change

y = final value

In mathematical terms, your final value can be described as thus:

y = x + x*p = x*(1 + p)

Since you are only looking for the percentage change, you must isolate (p).

Here are the steps to isolate (p):

y = x*(1 + p)

1 + p = y/x

p = (y/x) - 1

In ordinary words, the percentage change (p) should be:

Percentage Change = (Final Value / Starting Value) - 1

With this, you'd get a fraction which needs to be turned into a percentage that appeals to the human mind.

To spice up your final result, you can multiply by 100.

So you could say that:

p = [(y/x) - 1]*100

Or in words...

Percentage Change = [(Final Value / Starting Value) - 1]*100

Anyway, let me demonstrate how this would work in principle:

Here are your values:

Final Value = £8,400

Starting Value = £8,200

So, you could calculate the percentage change in this manner:

Percentage Change = [(£8,400 / £8,200) - 1]*100

Which is the same as:

p = [(y/x) -1]*100

Your result should be:

+2.44% (to 2 decimal places)

Now you can check this result and the power of the formula:

£8,200 * 2.44% = £200.08

The difference between £8,200 and £8,400 is exactly £200, so you can tell that the formula works.

This is the beauty of financial mathematics.

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