Currency growth rate (reverse)

Question

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?

Answer 1

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.

Answer 2

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.