Percent

Despite the fact that the calculation of interest in Soviet times, as far as I remember, was held in the 3rd grade, and now even earlier, there are people who could not learn the school curriculum.

These could be different reasons, which we will not talk about. I would like to say that a sufficiently large number of people in the modern world cannot allocate tax from the amount, subtract any percentage from the amount without using a calculator.

This only says unfortunately that the overwhelming majority of the population does not understand where the formula for allocating VAT (18%) from

where S is the sum

Therefore, a small definition:

Percentage (lat. Per cent - per hundred) - one hundredth of a share. It is indicated by the sign “%”. Used to indicate the proportion of something in relation to the whole.

It is logical to assume that if you understood all the words from the above definition, that 100% is what we have or what we want to take action on.

For example, we have 140 kilograms of salt (we take this for 100%). We need to take 13%

Making proportion

100% = 130 kg

13% = (X) how many kg?

Get X * 100% = 13% * 130kg

X = 130kg * 0.13 = 16.9 kg

With this sorted out now, consider the arithmetic operations with percentages.

To 130 kg of salt brought another 27% of the salt. How much salt has become.

27% of 130 kg is 0.27 * 130 (see the previous example) = 35.1 kg

that is, the answer is 130 + 0.27 * 130 or taking 130 out of the brackets we get 130 * (1 + 0.27) = 130 * 1.27 = 165.1 kg

It seems to be not at all difficult. Now subtracting from the amount of interest

Of 130 kg of salt, 45% was taken. How much is left?

45% of 130 kg is 0.45 * 130 = 58.5 kg

it means that 130-0.45 * 130 is left, or taking out 130, we get 130 * (1-0.45) = 130 * 0.55 = 71.5 kg

Now it remains to understand how financiers got that 18% of the amount should be considered according to the formula that was at the beginning of the article.

Let us formulate it this way:

We know the amount that includes the amount without tax and the amount of tax itself (18%).

that is, the amount = tax-free amount + tax amount

We want to know the amount of tax.

The solution is nowhere simpler, especially if we operate with numbers. So we have the amount with VAT (18%) = 13,000 rubles

What is the amount of VAT tax?

Obviously, the amount of tax = amount of tax-free * interest since the percentage is taken from some amount that we do not yet know and which we would also like to find.

Substituting the percentage we get the tax amount = tax-free amount * 0.18

that is, the sum = the sum of the tax-free + the sum of the tax-free * 0.18

and the amount is known and equal to 13000

then we get the equation with one variable 13000 = sum of tax-free (1 + 0.18)

and the amount of tax-free received 11,016.95 rubles

Now we have everything to find out the amount of tax

Amount = tax-free amount + tax amount

tax amount = 13000-11016.95 = 1983.05 rubles

Long, but very clear.

Now we abstract from specific numbers and do the same with the help of variables

Amount = tax-free amount + tax-free amount * 0.18 (tax)

tax-free amount = amount / (1 + 0.18)

Amount = tax-free amount + tax amount

Amount = Amount / (1 + 0.18) + Tax Amount

tax sum = amount-sum / (1 + 0.18) = amount * (1-1 / (1 + 0.18)) = amount * (1 + 0.18-1) / (1 + 0.18) = amount * 0.18 / 1.18

Multiply by 100 the numerator and denominator - we get the final formula of the sum-tax = sum * 18/118

So we got that magic formula by which accountants allocate VAT from the amount.

And replacing 18 with some other percentage, for example 10 or 27, we can also allocate the same amount of taxes

at 10% => total tax = amount * 10/110

at 27% => total tax = amount * 27/127

There is another Calculator with Interest on the website .  It allows you to solve the tricky problem of how many percent the value of the goods has changed, if at first the cost increased by 10%, and then decreased by 10%.

## Syntax

For XMPP client users: proc <amount> <percentage>

Each element is separated by at least one space.

## Examples

Purchasing manager, purchasing equipment from the manufacturer in the amount of 300 thousand rubles, asked for a "rollback" in the amount of 12% of the purchase amount.

Question: What real revenue will the manufacturer receive and what amount of “kickback” will he have to give to the “enterprising” procurement manager?

We write the request proc 300000 12

There are four possible answers in typical examples.

The amount of 300,000 includes a percentage of 12%
Then the amount without interest 267857.14285714
And the amount of interest 32142.857142857

The amount of 300,000 does NOT include a percentage of 12%
Then the amount with a percentage of 336,000
And the amount of interest is 36,000

The amount of 300,000 is a salary with deduction of tax of 12%
Then salary excluding tax 340909.09090909
And the tax amount is 40909.090909091

The percentage of 12% of the amount of 300,000 will be 36,000

Since the rollback percentage "hides" in total, then our decision

The amount of 300,000 includes a percentage of 12%
Then the amount without interest 267857.14285714
And the amount of interest 32142.857142857

That is, the procurement manager will receive a “remuneration” in the amount of 32,142 rubles, and the manufacturer will in reality sell the equipment to the customer at a price of 267,857 rubles, and not 300,000 as it went according to all accounting documents.

Costs of production using innovative technologies over the past year decreased by 20% compared with the previous one. This year, the costs amounted to 500 thousand rubles. What would be the cost of the enterprise this year if new technologies were not used?

We also write the request proc 500000 20

There are four possible answers in typical examples.

The amount of 500,000 includes a percentage of 20%
Then the amount without interest 416666.66666667
And the amount of interest 83333.333333333

The amount of 500,000 does NOT include a percentage of 20%
Then the amount with a percentage of 600,000
And the amount of interest is 100,000

The amount of 500,000 is a salary with deduction of tax 20%
Then the salary without tax 625000
And the tax amount is 125,000

The percentage of 20% of the amount of 500,000 is 100,000