# Currency growth rate (reverse)

For currency audusd:

On opening of Day1 the price is 20 and on closing of Day1 the price is 35

So the growth rate is (35-20)/20 = 0.75

So, for usdaud (reverse pair) the price at opening of Day1 will be 1/20 and the price at closing of Day1 will be 1/35

The growth rate now is (1/35-1/20)/(1/20) = -0.428

Is the calculation correct? Should the correct one be -0.75?

## 2 Answers

In general, if a quantity changes from $$x_{initial}$$ to $$x_{final}$$, the growth rate is $$\dfrac{x_{final} - x_{initial}}{x_{initial}}$$. So that calculation is correct.

A few things here. So your "growth rate" I am assuming is the percentage gained each day. Opening on Day 1 the value is 20, closing on Day 1 it is 35. That is an increase by 75%.

Now for the reverse pair, $$\frac{1}{20}$$ "grows" to $$\frac{1}{35}$$.

This implies that some growth rate $$R$$ has enacted upon $$\frac{1}{20}$$. i.e:
$$\frac{1}{20}\times R = \frac{1}{35}$$
$$\Rightarrow R = \frac{1}{20}\div\frac{1}{35}=\frac{20}{35}=\frac{4}{7}$$
This is taking $$\frac{1}{20}$$ and finding $$\frac{4}{7}$$ of it.
Or taking $$\frac{1}{20}$$ and reducing $$\frac{3}{7}$$ of it.
Or reducing $$\frac{1}{20}$$ by 42.9% (which is where your "-0.428" comes from)

You're answers are correct(-ish) they just need appropriate units. Remember a rate isn't just a number. It's usually a relationship between two units. I.e "$$\$$ 15 pr day" or "$$\$$ 20 increased by 75% during the day" are all valid rates of change.