How to calculate the percentage of the number of people. How to calculate the percentage of the total
How to calculate the percentage of the amount, you need to know in many cases (when calculating state fees, loans, etc.). We will show you how to calculate the percentage of the amount using a calculator, proportions and known ratios.
How to find out the percentage of the amount in general?
After that, there are two options:
- If you need to find out how much interest is another amount from the original, you just need to divide it by the amount of 1% obtained earlier.
- If you need the size of the amount, which is, say, 27.5% of the original, you need to multiply the size of 1% by the required number of percent.
How to calculate the percentage from the amount using the proportion?
But you can do it differently. To do this, you will have to use knowledge about the method of proportions, which is passed through the school mathematics course. It will look like this.
Suppose we have A - the principal amount equal to 100%, and B - the amount, the ratio of which with A as a percentage, we need to find out. We write down the proportion:
(X in this case is the number of percent).
According to the rules for calculating proportions, we get the following formula:
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X = 100 * B / A
If you need to find out how much the amount B will be with the already known number of percent of the amount A, the formula will look different:
B = 100 * X / A
Now it remains to substitute the known numbers into the formula - and you can make the calculation.
How to calculate the percentage of the amount using known ratios?
Finally, you can use more in a simple way... To do this, it is enough to remember that 1% as a decimal is 0.01. Accordingly, 20% is 0.2; 48% - 0.48; 37.5% is 0.375, etc. It is enough to multiply the original amount by the appropriate number - and the result will mean the amount of interest.
In addition, you can sometimes use simple fractions. For example, 10% is 0.1, that is, 1/10, therefore, to find out how much 10% will be, it's simple: you just need to divide the original amount by 10.
Other examples of such relationships would be:
- 12.5% - 1/8, that is, you need to divide by 8;
- 20% - 1/5, that is, you need to divide by 5;
- 25% - 1/4, that is, divide by 4;
- 50% - 1/2, that is, you need to divide it in half;
- 75% - 3/4, that is, you need to divide by 4 and multiply by 3.
True, not all simple fractions are convenient for calculating percentages. For example, 1/3 is close in size to 33%, but not exactly equal: 1/3 is 33, (3)% (that is, a fraction with infinite triples after the decimal point).
How to subtract a percentage of the amount without using a calculator
If it is required from already known amount to subtract an unknown number that is a certain amount of percent, you can use the following methods:
- Calculate an unknown number using one of the above methods, and then subtract it from the original.
- Calculate the remaining amount immediately. To do this, we subtract from 100% the number of percent that needs to be subtracted, and the resulting result is converted from percent to a number in any of the ways described above.
The second example is more convenient, so let's illustrate it. Let's say you need to find out how much will remain if you subtract 16% from 4779. The calculation will be like this:
- We subtract from 100 ( total percent) 16. We get 84.
- We consider how much will be 84% of 4779. We get 4014.36.
How to calculate (subtract) a percentage from a sum with a calculator in hand
All of the above calculations are easier to do using a calculator. It can be either in the form of a separate device or in the form of a special program on a computer, smartphone or ordinary mobile phone (even the oldest devices in use today usually have this function). With their help, the question of how to calculate the percentage of the amount is solved very simply:
- The initial amount is dialed.
- The "-" sign is pressed.
- The number of percent to be subtracted is entered.
- The "%" sign is pressed.
- The "=" sign is pressed.
As a result, the required number is displayed on the screen.
How to subtract a percentage from an amount using an online calculator
Finally, there are now enough sites on the Internet that offer an online calculator function. In this case, knowledge of how to calculate the percentage of the amount is not even required: all user operations are reduced to entering the necessary numbers into the boxes (or moving the sliders to get them), after which the result is immediately displayed on the screen.
This function is especially convenient for those who calculate not just an abstract percentage, but a specific size tax deduction or the amount of state duty. The fact is that in this case the calculations are more complicated: it is required not only to find the percentages, but also to add a constant part of the amount to them. The online calculator avoids such additional calculations. The main thing is to choose a site that uses data that complies with applicable law.
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The simplest and most intuitive method is proportioning. All further calculations take place on its basis. It looks like this:
- 45 is a known number equal to 100%.
- ? - a number that is 15% of 45.
Further, there is a simplification of the fraction to an equation with one unknown. According to mathematical laws, cross-sectional data in proportions are equal to each other, that is: 45 * 15% =? * 100%. To find "?", We use simple rule and we get the following.
The calculation of the proportion formula always occurs according to the principle of multiplying the known data, standing on the diagonal and dividing them by the third number.
You can compose a formula with any unknown in. In order not to be confused, percent or a number is obtained as a result, recall the rule of reduction in a fraction - if the percent sign (%) or monetary designation(rub) is present both above and below, it is reduced. Example:
The result of the calculation is the amount of money.
How to find the percentage of a number. Variants
Let us consider in order the situations of finding interest.
How to find 100%. It is necessary to calculate the number, 15% of which is equal to 45. We make the proportion:
Calculated by the formula: (45 * 100) / 15 = 300
If it is not known how much is 100%. Sometimes the calculation is carried out with respect to the same initial data, but their exact meaning is not known. For example: yesterday 15% of the total number of cookies in the amount of 450 rubles, and today 25%.
How much did you sell today? Since the amount for 100% is a common value for both 15% and 25%, it is possible to carry out calculations without looking for the full cost.
Calculated by the formula: (25 * 450) / 15 = 750
You can complicate the task if you are not sure of the calculations, or there is a need to check the result. To do this, first, be 100%, based on full data (15% costs 450 rubles), and then 25% is counted from 100%.
How much less than another number as a percentage
For example: the usual cost of a powder is 500 rubles. For the action, the price was reduced to 480 rubles. How much is the share price less than the original percentage? First, the percentage of the promotional price from the base price is found, and then their difference is found. We make the proportion:
We calculate by the formula: (480 * 100) / 500 = 96. 100% -96% = 4%. The share price is 4% less than the original one.
How much the number is greater than the other as a percentage. Example: the keyboard cost 300 rubles, and after the increase in the dollar rate, the price increased to 390 rubles. How much has the price of the keyboard changed in percentage? In the beginning there is a common interest rate new price, relative to the original, then their difference is calculated. We make the proportion:
We calculate by the formula: (390 * 100) / 300 = 130. 130% -100% = 30%. The price has increased by 30%.
The unknown number is higher than the known one by a certain percentage. Example: a product in a store is 15% more expensive than a product in stock. The price of sugar in the warehouse is 50 rubles and is equal to 100%. Shop price - 100% + 15% = 115%. Calculated by the formula: (115 * 50) / 100 = 57.5
The unknown number is less than the known number by the specified percentage. Example: wholesale is 5% cheaper. Retail price - 60 rubles and equal to 100 percent, for wholesale - 100% -5% = 95%. We make the proportion:
Calculated by the formula: (60 * 95) / 100 = 57
Percentage between two numbers. The situation when a number is known that is 100% and a number that is a certain fraction of the original. Example: a batch of 60 boxes was expected, but 53 were delivered. What percentage of the plan was fulfilled. We make the proportion:
Calculated by the formula: (53 * 100) / 60 = 88.3
The most difficult "task" is not to get confused in the proportion.
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The percentage (or ratio) of two numbers is the ratio of one number to another multiplied by 100%.
The percentage of two numbers can be written using the following formula:
Percentage example
For example, there are two numbers: 750 and 1100.
The percentage of 750 to 1100 is
The number 750 is 68.18% of 1100.
The percentage of 1100 to 750 is
The number 1100 is 146.67% of 750.
Example task 1
The vehicle manufacturing plant has a production rate of 250 vehicles per month. The plant assembled 315 vehicles in a month. Question: by what percentage did the plant exceed the plan?
Percentage of 315 to 250 = 315: 250 * 100 = 126%.
The plan was fulfilled by 126%. The plan was overfulfilled by 126% - 100% = 26%.
Example task 2
The company's profit for 2011 was $ 126 million, in 2012 the profit was $ 89 million. Question: by what percentage did profit fall in 2012?
The percentage of 89 million to 126 million = 89: 126 * 100 = 70.63%
Profit fell by 100% - 70.63% = 29.37%
The very concept of interest must be familiar to many, but for some reason difficulties arise in the calculations associated with them. And such problems occur not only among young children, but even among successful adults. Someone may argue that he does not need interest in life, since he does not meet with them anywhere. But this is absolutely not the case. All tax rates, including income tax(Personal income tax), VAT, etc. calculated as a certain percentage of the number. The situation is the same with loans, which are used by the majority of citizens. That is why it is necessary to know how to calculate the interest correctly, so as not to be deceived in the modern world.
General case of computation
- Find 1% of the number. To do this, simply divide the known value by 100%.
- Then we multiply the resulting result by the value that needs to be found.
If it's not clear in words, let's give a simple example: VAT is 20% of the value of goods. It is said that the price of goods without VAT is 300 rubles. How much will the tax itself be?
The calculation is carried out as follows:
- We find 1%: 300/100 = 3 rubles.
- Determine 20% of 300: 3 rubles. * 20% = 60 rubles.
Now someone who understands the issue may be surprised and ask why such difficulties, because you can do it in a completely different way: 300 * 0.2 = 60 rubles. It is possible and so, but for some reason not everyone understands that first it is necessary to convert the value in "%" into a coefficient, and then multiply the number by it. Everybody does it the way it is convenient for him and how he was taught at school. Both options are valid.
But a completely different situation may arise: it will be necessary to determine how much% is a certain value of a certain amount. In this case, the calculation algorithm is completely different:
- It is again necessary to find 1% of the known number by dividing by 100%.
- Then it will be necessary to divide the desired digit by the resulting number.
For example, we give the opposite situation. It is known that the VAT is 60 rubles. The price of the goods is 300 rubles. What is the value added tax rate?
Payment:
- Find the same 1%, it will be UAH 3.
- Divide 60 by 3 to get 20%.
As you can see, everything is very simple, the main thing is to understand the algorithm. It is extremely difficult to make a mistake.
Interest calculation is necessary in different areas of life.
How to count using proportion
Everyone should know the rule of proportion, which everyone loved so much in mathematics lessons. We recall the well-known X. In order to recall the rule of proportion, let us give an example: wage in the amount of RUB 10,000, personal income tax rate- 15%. It is necessary to determine how much a person actually receives on a card account.
We get the following:
10000 – 100%;
X - 15%
We find X = (10000 * 15) / 100 = 1500 - this is the amount of personal income tax that will be retained from the employee. Consequently, the salary to be paid will be 10,000 - 1,500 = 8,500 rubles.
Calculation in Excel
It's hard to find a modern person who doesn't use software... And one of those commonly used programs is excel. In order to calculate percentages using this program, you must be able to correctly determine the formulas to calculate what you need to find.
If you need to find: how much a specific number is of the total, then you need to enter the value in the cell after the "=" sign: Private / General. You do not need to divide or multiply by 100, just for the cell where the calculation is carried out, you need to set the percentage format of the number. In this case, instead of indicators in Excel itself, the formula will contain the name of the cells, for example, A2 / B2.
In economics, it is often necessary to calculate the share of each number from the total value, for example, how much each item of income occupies in overall size income. In this case, the formula in Excel will look the same, in the numerator - the quotient, in the denominators - the general, only the denominator itself will be permanently fixed. It's easy to do with the $ icon. The formula is: A2 / $ B $ 2.
There are often times when it is necessary to calculate the growth rate or growth rate of a certain indicator. In this case, the formula will look completely different:
- if the growth rate is found, then the following formula is written in the cell: Value of the current period / Value of the previous one. And you need to set the percentage format;
- if the growth rate is found, then the formula is as follows: (Value of the current period - Value of the previous period) / Value of the previous period.
Loan rate: calculation options
Considering also the question of how interest is calculated, one cannot fail to mention credit rate... This is the most common practical way in which people start calculating a given quantity using mathematical techniques.
For some reason, many people think that it is quite easy to perform mathematical operations. For example: if it is known that the loan amount is 10,000 rubles, and it is taken for 1 year, the rate is 10 percent, then the calculation is as follows: 10,000 / 0.1 = 1000 is the payment for a year of using the loan. If we divide by 12 months, we get monthly amount overpayment for a loan.
But in fact, a completely different calculation algorithm. It all depends on what method of accrual is used, on how the rate is calculated - every day, monthly or annually. And further we will talk in more detail about credit settlements.
Loans are calculated according to the annuity and differentiated system
Differentiated settlement system
This profitable system for the borrower himself, since it saves on the amount of overpayment. Why is it so? Yes, because first everything goes to repay the loan body, and then to interest. In this case, the rate itself is applied to the balance of debt on loans. Such a scheme is characterized by the fact that first the borrower pays the maximum allowable payments, and only then the lowest.
In this case, both the formula of simple and compound interest... The only difference is when and how often they are charged.
We note right away: the use of simple calculations is very rarely used by the bank, since it is unprofitable for the lender himself.
The bottom line is that the overpayment is charged once at the end of the term.
Fv = Sv * (1 + R * (Td / Ty))
- Fv- the amount that the borrower must pay at the end of the term;
- Sv- the size of the loan itself issued to the borrower by the bank;
- R- the rate specified in the contract;
- Td- term. It may be in days in months, blocks(it all depends on the period for which the overpayment is charged);
- Ty- the number of those periods per year that are used in the calculation. It can be 365 days, 12 months, 4 quarters, or just 1 year.
For example, let's present a calculation. Note that this formula can be used both for a loan and for a deposit. No difference.
Example: The borrower was given money in the amount of 1,000 rubles. for 10 months at 10% per annum with a monthly charge. We get the following calculation: the amount to be returned = 1000 * (1 + 0.1 * (10/12)) = 1083 rubles. For use credit funds client pay 81 rubles.
The calculation of such a plan is mainly used when calculating deposit payments, since it is profitable for the bank to accrue the client's income once, without using complex calculations.
Compound interest
It should be said that such a technique is quite complicated, its essence lies in the fact that when determining the amount of overpayment, it is necessary to take into account the existing capitalization. This means that the accrued amount of income is added to the initial amount, and then profit continues to accrue on this amount.
When lending, this technique is very rarely used, only if the client has not fulfilled his obligations on time, and the amount of interest, fine, mandatory payment for the month is added to the principal amount of the debt and the rate is charged on it.
Calculation of capitalization of interest on deposits
Speaking about this method, special attention should be paid to capitalization. It is when calculating it that you can find out how to calculate percentage by percentage. Capitalization is not carried out regularly, but only at regular intervals. This frequency is determined by the terms of the loan or deposit agreement. For example, on a deposit, interest is paid to the client once a year, and only if at the end of the year he does not take them, they will automatically be credited to the deposit. And already in the second year, the profit will be accrued on the total amount. For this, the following formula is used:
Fv = Sv * (1 + (R / Ny)) Nd,
- Fv capitalized value;
- Sv- initial deposit or loan;
- R- annual rate;
- Ny- the number of periods for which capitalization will be carried out within one year;
- Nd- total number of capitalized periods
For understanding, we will again give a clear example: a bank client decided 10,000 rubles. place on a deposit at 12% per annum. Capitalization is monthly, and the term of the deposit is one year.
The calculation will be as follows: 10000 * (1 + 0.12 / 12) * 12 = 11268.
This means that the client, together with his deposit, as a result of the withdrawal of the entire amount from the account, will be able to receive 11268 rubles. At the same time, the net profit will amount to 1268 rubles. (11268-10000).
If we consider two calculation schemes, then for those who invest in a deposit account, a complex technique is more profitable, since frequent capitalization allows you to increase the basis for calculation. A simple technique is more convenient for loans. But the choice is still up to the bank, not the borrower or the client.
Annuity Scheme
Regarding, there is no fundamental difference in the calculation method: both a simple and a complex formula can be used. The bottom line is that the amount of interest and the principal amount of the debt are distributed in equal parts. Repayment is made monthly.
But to be honest, the borrowers themselves very rarely use these formulas, since on every bank website and just on the Internet there is credit calculator, where you can enter the data, easily and quickly get the desired result.
Thus, at first glance, it seems that the calculation of interest is not needed for Everyday life and many do not pay attention to this moment. But in order to be economically literate and choose the most profitable options, you need to know this.
Mathematics is not just a science that lives within school walls. It is used daily in household items for various calculations. Especially often you have to find the percentage of the number - this is necessary when buying goods by weight, when paying taxes, when going to a restaurant. It is extremely important to be able to quickly and correctly make such calculations.
Mathematicians represent a quantity as an integer, i.e. it has full 100%, and some fraction of a given value is its hundredth part. Thus, a percentage is a hundredth of some full value.... For example, 1 kilogram is 100%, and half a kilogram is 50%.
It's important to know! Shares on paper are always recorded with a "%" sign.
Fractions can always be represented as decimal fractions: 1% = 1/100 parts = 0.01, which is very convenient when calculating manually. To determine 1% of any value, I always take it as 100%, then 1% will be unknown, which is 100 times less.
It is convenient to determine the percentage of the number using proportions. Let it be necessary to take and find 1 percent of the number 349, where:
You should be careful here, because you can get confused about which is which. To avoid this, you should always write percentages (%) on one side. It is best to make the proportion in a column - then it will be more convenient to determine the percentage of the number. Find x using the cross rule:
If you know the relationship of fractions with decimal fractions, then it will be even easier to count, since it is enough to separate two digits from the end of the digit with a comma to select it 1%. For example, 1% of the number 248 will be equal to 2.48, and to calculate 7% from it, it will be enough to multiply the found 1% by 7 = 2.48 * 7 = 17.36.
Basic formulas
There are several basic formulas for solving fractional equations.
How to find a number by its fraction? If the value of X is known, which is several fractions of Y, and it is necessary to find the value of the unknown Y, then the expression is solved using the formula:
How to find the expression of one quantity from another in%? If the values of Y X are known, but it is necessary to find the part that makes up the number X, then this can be represented as an expression:
These three formulas are most common when solving various fractional equations, so it is important to memorize them and learn to apply them quickly.
Using calculators
Modern technology makes it possible not to calculate percentages of numbers on your own, using the technique. You can use a regular electronic calculator with interest. To make sure that the device fits, you need to find a button with a% icon on it, such are usually found among the multiplication-division actions. After that, you can start calculating.
Good to know! The ancestor of the calculator was the summing machine, which was created by the great mathematician Blaise Pascal.
The device looked like a box with gears inside.
How do I find the percentage of a number? For example, a value that is 17% of 123. Using a calculator, you can calculate:
- Dial 123 so that it is displayed on the scoreboard.
- Select the action to multiply (X).
- Then enter 17 and click on the corresponding button (%).
- The answer will be displayed on the scoreboard - 20.91.
This algorithm is used to find answers to any expressions with the calculation of fractions and hundredths. But another convenient method is to use an online calculator. To solve the problem, it is enough to go to the site of such a calculator by entering its address into the browser line or by entering a request in a search engine.
An online calculator is a page on a site where there are windows where you need to enter values. Usually, in front of the window, it is written what action the calculator performs (finds the% of the quantity, the quantity by%, etc.), so you need to choose the right one. It is enough to enter the values in the appropriate windows and click on the "Solve" button ("Find", "Calculate", etc.), the calculator will give the answer.
Useful video
Let's summarize
- The use of customer-supplied raw materials for the production of finished products: accounting, consumption rates, write-off Reflection of services for the processing of materials
- Terms of payment of insurance premiums and submission of reports under the new rules
- Reminder of admission to off-budget (paid) places How to pay for tuition
- Online courses for accountants, distance accounting courses online, online training for accountants Accounting for cash transactions and transactions with accountants