Future value with compound interest
If you'd like to know what an investment could be worth in the future, with compound interest, you'd use this equation:
FV = PV x (1+r)^n
Where:
FV = Future value
PV = Present value
r = interest rate per period
n = number of periods
In this case, PV, r, and n are independent variables because you can make them anything you want to generate FV. So, it doesn't matter what you make those variables; they will not affect one another -- only FV.
P/E ratio
The P/E ratio also uses independent variables, which are price and earnings per share (EPS). The equation is:
P/E ratio = Price / EPS
In this case, price and EPS are the independent variables. If you change one, the other won't change. The only thing that changes in the equation is the P/E ratio.
Independent variables versus dependent variables
The easiest way to tell between an independent variable and a dependent one is whether or not they will change if something else changes in the equation. In the above examples, you can see that the dependent variables, often on the left side of the equation, change when the independent ones are manipulated, but the independent variables don't change unless you change them.
You can make the independent variables anything, and they won't budge, but every change to an independent variable will have an effect on the dependent one. Let's look at an example.
If you're looking at a P/E ratio, for example, P/E ratio is your dependent variable -- it changes as you change price and EPS.
- If the price is $10 and EPS is $1, the P/E ratio will be 10.
- If the price is $10 and EPS is $5, the P/E ratio is now 2.
- But, if the price goes to $15, EPS can stay at $5, and only the P/E ratio will change, to 3.
That's how independent and dependent variables interact.