I have a very simple yet somehow confusing question regarding percentage increases/decrease. I am a bit confused about my initial approach for determining percentage difference between two values versus just being just given the easy formula. Without actually knowing the equation by heart this was my initial approach.
If I have an old value A = 350 and a new value of B = 371. What is the percent increase? So I approach this problem in this way
A/B = 0.943397 so it take 4 decimal places.
I then take 1-0.943397 = 0.56603 x 100 = 5.6603 percent increase. Therefore (5.6603 * 1/100) * 371 = 21 and this checks out.
But if I use the New Value – Old Value / Old Value I get 6 percent. Where is this error coming from?
Best Answer
You fell in the trap. A relative change can be computed wrt the old value or the new value, you need to be specific about that.
$$\frac{371-350}{350}=\frac{371}{350}-1=6.00\%$$
$$\frac{371-350}{371}=1-\frac{350}{371}=5.66\%$$
For a similar reason,
$$\begin{align}100+10\%&=110,\\110-10\%&=99\ !?!\end{align}$$