General formula - % of %

Question

I would like to find a way to represent the following idea in a general formula:

I have 100%, then I subtract 2% from it. Now I have 98% of the original value and subtract 4% from it, which leaves me with 94.08%.

Basically, it is something like:

Result = (1 - sub1) - sub2, where sub 1 is 2% and sub2 is 4%.

I ask that because I would like to apply more iterations to it, so I could express it mathematically using some general formula.

*P.S.: I want to know if there is a way to represent that mathematically.

Answer 1

You might consider a straightforward relation between calculating percentages and simply multiplying by an adequate factor. Readily, when you want to obtain the $p$% of $C$, you just multiply by $\frac{p}{100}$.

Now, substracting 2% from $C$ means getting a 98% of it, so in this case your result $R$ is $$ R = C \cdot \frac{98}{100} = C \cdot 0.98 = C\cdot (1-0.02). $$

So the formula you are interested in is $$ R = C \cdot (1-0.02)(1-0.04)\dots $$ whatever you decide for your sequence of percentages.

Answer 2

With $S_1$ and $S_2$ being your percentage values, the general formula is:

$$\frac{100-S_1}{100}\cdot\frac{100-S_2}{100}$$

With $S_1,\dots,S_n$ being your percentage values, the general formula is:

$$\prod\limits_{i=1}^{n}\frac{100-S_i}{100}$$