Since childhood, the notion of finances is important, even if simple. The starting point is to learn about percentage increases and discounts. This concept can be applied to the price of goods, among others.

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Correction factor

The beginning of the concept of increase and discount is given by a correction factor, applied to the price or to something that is increased or decreased.

Let $p$ be the percentage applied to the price of the merchandise. Thus, the correction factor $f_c$ is given by:

$$f_c = (1+p) \qquad \text{aumento}$$ Board. $$f_c = (1-p) \qquad \text{desconto}$$ Board.

Increase

So far, we have seen that the correction factor for an increase in capital or merchandise is given by:

$$f_c = (1+p)$$

But how do we arrive at this correction factor?

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Let $c$ be the initial capital we have so far and $p$ be the percentage applied to this capital. To increase capital we have:

$$ \begin{aligned} c_f &= c + p ~.~ c\\ &= c(1+p)\\ \end{aligned} $$
  • $c_f$: final capital;
  • $c$: initial capital;
  • $p$: percentage applied to the initial capital;
  • $1+p$: correction factor for increase.

Example of video game price increase

A video game that cost BRL 1000.00 reais suffered an adjustment (increase) of 15% according to inflation during the period. What is your current price?

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Response:

$$ \begin{aligned} c_f &= c(1+p)\\ &= 1000 (1+15\%)\\ &= 1000 (1+\dfrac{15}{100})\\ &= 1000 (1+0.15)\\ &= 1000 (1.15)\\ &= BRL~ 1150\\ \end{aligned} $$

The video game underwent an adjustment of BRL $150.00$, with a final price of BRL $1150.00$.

Discount

Now let’s define the correction factor for discounting a capital or commodity is given by:

$$f_c = (1-p)$$

But how do we arrive at this correction factor?

Board.

Let $c$ be the initial capital we have so far and $p$ be the percentage applied to this capital. For capital discount we have:

$$ \begin{aligned} c_f &= c - p ~.~ c\\ &= c(1-p)\\ \end{aligned} $$
  • $c_f$: final capital;
  • $c$: initial capital;
  • $p$: percentage applied to the initial capital;
  • $1-p$: correction factor for discount.

Example of TV price discount

Lucas wants to buy a new television for anime. She decides to buy a Smart TV and searches the internet to find the price. He discovers that the value of the television is BRL 1600,00. When you go to the physical store, you discover that the television has a discount of 30%. Calculate how much he will pay for the television.

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Response:

$$ \begin{aligned} c_f &= c(1-p)\\ &= 1600 (1-30\%)\\ &= 1600 (1-\dfrac{30}{100})\\ &= 1600 (1-0.30)\\ &= 1600 (0.70)\\ &= BRL~ 1120\\ \end{aligned} $$

Smart TV had a discount of BRL $ 480.00$, with a final price of BRL $1120.00$.

These are the concepts of discounts and increases. Wait for the next posts.