Monthly change formula logic.

Question

I need an explanation of the formula: monthlyChange=(newValue-oldValue)/oldValue Why to divide by old value? Apparently the difference is described well just via subtracktion "newValue-oldValue".

Answer 1

There exist different concepts changes:

1. $\text{Absolute change=AC=newValue-oldValue}$

Let´s inspect two cases:

a) $AC_1\text{=130-100}=30$

b) $AC_2\text{=30-10}=20$

Here $AC_1\color{red}>AC_2$.

2. Now we calculate the relative change, $RC$.

a) $RC_1=\frac{\text{130-100}}{100}=0.3=30\%$

b) $RC_2=\frac{\text{30-10}}{30}=\frac23\approx 66.67\%$

Here we have $RC_1\color{red}<RC_2$

These two concepts of measuring changes can result in different relations, but it must not. It depends on the context which concept is appropriate.