What is percentage? Interest formula. Percentages - how to calculate? How to find the percentage of a number? Basic problems for finding percentage

Percentage shows the hundredth part of a unit, which is indicated using the “%” sign. This indicator is used to indicate the proportion of something to the whole. They still knew how to calculate the percentage of a number Ancient Rome. Before the decimal system was invented, calculations were made using fractions that were divisible by 1 to 100. Octavian Augustus imposed a tax of one hundredth on goods that were sold at auction, called Centesima Rerum Venalium. Calculation using multipliers was somewhat reminiscent of calculating percentages.

When currency was replaced in the Middle Ages, calculations with the denominator one hundred became more common, and from the late 16th century to the early 17th century, this method of calculation began to be used by everyone, based on materials that contained arithmetic calculations. According to the materials, this method was used when calculating profit and loss, interest rates, as well as rule of three. In the seventeenth century, this form of calculation was the standard for expressing interest rates in hundredths. The concept of interest was introduced in Russia by Peter I. However, it is believed that similar calculations began to be used in the Time of Troubles, as a result of the first pegging of minted coins at 1 to 100, when the ruble was worth 10 hryvnias, and a little later - 100 kopecks.

Sometimes two quantities are compared not by comparing their values, but by percentage. For example, compare the price of two goods not in monetary terms, but compare as a percentage how much the price of one product exceeds the price of the other. If it is possible to determine how much one indicator is more or less than another, then for comparison in % it is necessary to indicate relative to what value the percentage is calculated. Such an indication is sometimes not necessary when it is said that one indicator is greater than another by a percentage that is greater than 100. In this case, there is one way to find the percentage, divide the difference by the smaller of the two numbers and multiply this number by 100.

How to find the percentage of a number

In order to find the percentage of a number, you need to multiply the given number by the number of percentages and divide the resulting number by one hundred. As a rule, there are three main types of problems for calculating percentages:

• Calculate the percentage of this number. This number must be multiplied by the specified percentage, and then the result must be divided by 100.
• Determine a number from a given other number and its value as a percentage of the desired number. This number must be divided by the percentage and the result multiplied by 100.
• Determine the expression of one number from another as a percentage. The first number must be divided by the second and the result multiplied by 100.

As a rule, in an economy where most indicators are expressed as percentages, the change in such indicators is expressed not as a percentage of the original indicator, but in percentage points, which show the difference between the new and old values ​​of the indicator. For example, if in a country the business activity index increased from 50% to 51%, then its changes are calculated in the same way: (51%-50%)/50= 1/50=2%, which in percentage points is 1%.

We were often told at school that mathematics would be useful to us in life. This is partly true. Integrals and limits are not useful to us in life, but we have to count money every day. Most often in monetary transactions the concept of interest appears. Today you and I will learn to find them.

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What is interest?

This word comes from the English phrase Pro Centum. After reading this phrase, you probably noticed that the word cent is present there. This is where the meaning of percentage comes from. As you know, a cent is one hundredth of a dollar. Therefore, 1% is one hundredth of the number.

Nowadays, many financial indicators are measured as percentages:

1. taxes;
2. shares in business;
3. return on investment;
4. bonuses and fines;
5. inflation.

And not only financial:

1. fertility and mortality;
2. statistics of successful and unsuccessful marriages;
3. efficiency.

Let's take a closer look at how to calculate the percentage of the amount. We will give you some examples to help you understand everything.

Example 1. The taxi driver has completed his shift. For the day, his revenue amounted to 5 thousand rubles. He needs to give the taxi service a commission on these orders - 15%. To find out the amount the driver must pay, you need to multiply 5 thousand by 15, then divide by 100. We get a result equal to 750 rubles. As you may have guessed, 15% is 15 parts out of a hundred.

Now we will give you the opposite example with the same taxi driver. So, during his shift he earned 5 thousand rubles. He spent a certain part of this money on mandatory expenses:

1. taxi service commission - 750 rubles;
2. car wash - 250 rubles;
3. fuel - 1 thousand rubles.

In total, the driver has 3 thousand rubles left. Of the 5 thousand rubles he earns, he takes only 3 for himself. Now our task is to calculate what part of the total revenue he can safely put in his pocket. To do this, we need to divide 3 thousand by 5 thousand. Then multiply the resulting result, equal to 0.6, by 100%. It turns out that the driver pockets 60% of the total revenue.

Example 2. Four shareholders started the business. After a year of hard work, it began to generate income. The partners decided to divide the profits equally, that is, each will get 25% of the profits. We need to calculate how much money each of them will receive.

Let’s say a business brings in an income of 200 thousand rubles per month. To calculate the profit of each shareholder, you need to multiply 200 thousand by 25, and divide by 100. We get the result - 50 thousand rubles.

Example 3. Sales conversion. A sales manager offers his company's services over the phone. He made 800 calls in a month. 280 clients were interested in the company's services. To calculate sales conversion, you need to divide 280 by 800, then multiply by 100. The result will be 35%.

Tricks for finding percentages

1. field for entering a percentage;
2. a field for entering a number, the percentage of which we will find;
3. "Calculate" button.

You can easily find such a calculator on the Internet; you don’t have to bother with calculations. In principle, it is logical to use all the benefits of the Internet. However, there are situations in life when you need to calculate the percentage of a number, but you don’t have a calculator at hand.

You can find online calculators on the following sites:

1. calculator888.ru;
2. fin-calc.org.ua;
3. calc.by.

If you need to find 20 or 40%, multiply the amount by 0.2 and 0.4 respectively.

A very simple technique for finding percentages is division.. But it can only be used with numbers that are easily divisible by 100. For example, 100 is easily divisible by 25. The result of division is four. This means that to find 25% of the amount you simply need to divide it by 4. Using the same scheme, you can find 10, 20 and 50% of the amount you need.

Knowing how to calculate interest on interest will help you plan your income. For example, with a deposit with an interest rate of 10% per year, your income for 2 years will be 21%. Because in the second year interest was already accrued on the amount accumulated during the first year. And this is 110% of the down payment amount.

Conclusion

In conclusion, I would like to say that knowing how to calculate the percentage of a number will help you in life. After all, they won’t be able to deceive you when selling goods and when issuing wages. You are given a certain percentage of the money you earned. Don't be shy about asking your boss for pay slips. Carefully check and recalculate all payment documents, because you may be deceived. As they say: “Trust, but verify!”

Example 1

You go to the supermarket and see a promotion for . Its regular price is 458 rubles, now there is a 7% discount. But you have a store card, and according to it, a pack will cost 417 rubles.

To understand which option is more profitable, you need to convert 7% into rubles.

Divide 458 by 100. To do this, you simply move the comma separating the integer part of the number from the fractional part two positions to the left. 1% is equal to 4.58 rubles.

Multiply 4.58 by 7 and you get 32.06 rubles.

Now all that remains is to subtract 32.06 rubles from the regular price. According to the promotion, coffee will cost 425.94 rubles. This means that it is more profitable to buy it with a card.

Example 2

You see that the game on Steam costs 1,000 rubles, although it was previously sold for 1,500 rubles. You are wondering what percentage the discount was.

Divide 1,500 by 100. Moving the decimal point two places to the left gives you 15. That's 1% of the old price.

Now divide the new price by 1%. 1,000 / 15 = 66.6666%.

100% – 66.6666% = 33.3333%. This discount was provided by the store.

2. How to calculate percentages by dividing a number by 10

You first find the 10% rate and then divide or multiply it to get the percentage you need.

Example

Let's say you deposit 530 thousand rubles for 12 months. The interest rate is 5%, capitalization is not provided. You want to know how much money you will get in a year.

First of all, you need to calculate 10% of the amount. Divide it by 10 by moving the decimal place one place to the left. You will receive 53 thousand.

To find out how much 5% is, divide the result by 2. That's 26.5 thousand.

If the example was about 30%, you would need to multiply 53 by 3. To calculate 25%, you would have to multiply 53 by 2 and add 26.5.

In any case, it is quite easy to operate with such large numbers.

3. How to calculate percentages by making a proportion

Making proportions is one of the most useful skills taught to you in . You can use it to calculate any percentage. The proportion looks like this:

amount constituting 100% : 100% = part of the amount: share as a percentage.

Or you can write it like this: a: b = c: d.

Typically, proportion is read as “a is to b as c is to d.” The product of the extreme terms of a proportion is equal to the product of its middle terms. To find out the unknown number from this equality, you need to solve the simplest equation.

Example 1

For an example of calculations, we use the recipe. You want to cook it and bought a suitable 90 g chocolate bar, but you couldn’t resist taking a bite or two. Now you only have 70g of chocolate and you need to know how much butter to put instead of 200g.

First, calculate the percentage of chocolate remaining.

90 g: 100% = 70 g: X, where X is the mass of the remaining chocolate.

X = 70 × 100 / 90 = 77.7%.

Now we make a proportion to find out how much oil we need:

200 g: 100% = X: 77.7%, where X is the required amount of oil.

X = 77.7 × 200 / 100 = 155.4.

Therefore, you need to put approximately 155 g of butter in the dough.

Example 2

The proportion is also suitable for calculating the profitability of discounts. For example, you see a blouse for 1,499 rubles with a 13% discount.

First, find out how much a blouse costs as a percentage. To do this, subtract 13 from 100 and get 87%.

Make up the proportion: 1,499: 100 = X: 87.

X = 87 × 1,499 / 100.

Pay 1,304.13 rubles and wear the blouse with pleasure.

4. How to calculate percentages using ratios

In some cases, you can use simple fractions. For example, 10% is 1/10 of a number. And to find out how much it will be in numbers, just divide the whole by 10.

• 20% - 1/5, that is, you need to divide the number by 5;
• 25% - 1/4;
• 50% - 1/2;
• 12,5% - 1/8;
• 75% is 3/4. This means you have to divide the number by 4 and multiply by 3.

Example

You found trousers for 2,400 rubles with a 25% discount, but you only have 2,000 rubles in your wallet. To find out if you have enough money for a new thing, carry out a series of simple calculations:

100% - 25% = 75% - the cost of the trousers as a percentage of the original price after applying the discount.

2,400 / 4 × 3 = 1,800. That’s how many rubles the pants cost.

5. How to calculate interest using a calculator

If life is not pleasant for you without a calculator, all calculations can be done with its help. Or you can do it even simpler.

• To calculate a percentage of an amount, enter the number equal to 100%, the multiplication sign, then the desired percentage and the % sign. For the coffee example, the calculation would look like this: 458 × 7%.
• To find out the amount minus interest, enter a number equal to 100%, a minus, the size of the percentage and the % sign: 458 - 7%.
• You can add up similarly, as in the example with a deposit: 530,000 + 5%.

6. How to calculate interest using online services

The site contains various calculators that calculate not only percentages. There are services for lenders, investors, entrepreneurs and all those who do not like to do math in their heads.

In mathematics, a percentage is one hundredth of a number. For example, 5% of 100 is 5.
This calculator will allow you to accurately calculate the percentage of a given number. There are various calculation modes available. You will be able to produce various calculations using percentages.

• The first calculator is needed when you want to calculate the percentage of the amount. Those. Do you know the meaning of percentage and amount?
• The second one is if you need to calculate what percentage X is of Y. X and Y are numbers, and you are looking for the percentage of the first in the second
• The third mode is adding a percentage of the specified number to the given number. For example, Vasya has 50 apples. Misha brought Vasya another 20% of the apples. How many apples does Vasya have?
• The fourth calculator is the opposite of the third. Vasya has 50 apples, and Misha took 30% of the apples. How many apples does Vasya have left?

Frequent tasks

Solution: We use the first calculator. Enter the bet 6 in the first field, 100000 in the second
We receive 6,000 rubles. - tax amount.

Problem 2. Misha has 30 apples. He gave 6 to Katya. What percentage of the total number of apples did Misha give to Katya?

Solution: We use the second calculator - enter 6 in the first field, 30 in the second. We get 20%.

Task 3. At Tinkoff Bank, for replenishing a deposit from another bank, the depositor receives 1% on top of the replenishment amount. Kolya replenished the deposit with a transfer from another bank in the amount of 30,000. What is the total amount for which Kolya’s deposit will be replenished?

Bank interest calculators

Calculation algorithms

• Subtract the final price from the initial price and determine the discount in rubles C = 50 - 30 = 20
• Discount in rubles C divided by the starting price A and multiplied by 100%, Discount percentage = 100* 20/50 = 40%