How to calculate percentages basic rules. How to calculate the percentage of the amount? Increase, decrease a number by a specified number of percent
The concept of% (share) of something
Interest history, interest calculation, recruitment rules, colloquial use, interest tasks
Percentage is, definition
Concept percent
History of origin percent
Using interest in everyday life
Interest task types
Interest calculations
Percentage in programming
Percentage is, definition
percent Is one hundredth. It is denoted by the "%" sign. Used to indicate the proportion of something in relation to the whole. For example, 17% of 500 kg means 17 pieces of 5 kg each, that is, 85 kg. This mathematical concept is often found in everyday life. The etymology of the term has Latin roots. The word "percentage" comes from the Latin word pro centum, which literally translates "for a hundred" or "from a hundred."
As an economic concept in the meaning of "", " benefit", the word" advantage "began to be used in the second half of the 19th century.
Financial definition of interest - a fee that one person () transfers to another person ( borrower) for the fact that the latter provides the former with funds for temporary use.
In modern financial lexicon, interest is defined as payment for the use of borrowed funds, as rental income. When financiers talk about interest, they mean redemption, that is, such a rate in the discount coefficient that equalizes the discounted (reduced) the price future results with its present price.
Business vocabulary - to work for interest means to work for a remuneration calculated depending on arrived or turnover. In this regard, the percentage acts as a commission that characterizes, first of all, the work of the broker.
Percentage concept
In the text, the percent sign is used only for numbers in digital form, from which it is separated by a non-breaking space (67%) when typing, except when the percent sign is used to abbreviate complex words formed with the numeral and the adjective "percent"
percentage in Chinese is denoted by different words depending on whether it is used in mathematical or economic sense. In its pure form, "percentage" is 百分比 (bifenbi), which literally translates as "ratio to a hundred parts." So, for example 10% would sound like "ten hundredths". That is, in the Chinese percentage there is necessarily a mention of "one hundred" and there are no extraneous borrowed or ancient words, but only pure mathematics.
In the economic sense, interest is "benefit." Accordingly, the word 利率 (lilu) is used. The first hieroglyph is "profit", the second is "coefficient", that is, "coefficient of profit". The word itself can be translated as "percentage, percentage (to capital), rate of profit".
Percentage in China is often used in expressions like "over the past year, the country began to generate 9% more electricity." Moreover, both the percent sign "%" and the literal spelling of the expression "nine hundredths" can be used.
0,07 % = 0,0007;
The rule for writing the number and the percent sign was separately introduced in 1982 by the normative document GOST 8.417-81 (subsequently replaced by GOST 8.417-2002); it was previously the norm not to separate the percent sign with a space from the preceding digit.
Currently, the rule of skipping the percent sign is not generally accepted. Until now, many Russian publishers do not follow the recommendations of GOST 8.417-2002 and still adhere to the traditional typing rules, that is, when typing, the percent sign is not separated from the preceding number.
Sometimes it is convenient to compare two values not by the difference in their values, but in percentages. For example, the price to compare two goods not in rubles, but to evaluate how much one product is more or less than the price of the other in percentage. If the comparison by difference is completely unambiguous, that is, it is always possible to find how much one value is greater or less than another, then for comparison in percentage it is necessary to indicate with respect to which value the percentage is calculated. Such an indication, however, is not necessary in the case when it is said that one value is greater than the other by a number of percentages exceeding 100. In this case, there remains only one possibility of calculating the percentage, namely, dividing the difference between the smaller of the two numbers and then multiplying the result by 100.
Interest in the economy
interest is part of the profit that creditor pays the borrower for the borrowed money capital, and is defined as the "irrational form of the price" of the loan capital... The source of interest is the surplus value created in the process of productive use of the loan capital... The division of the profit obtained from the use of loan capital into the interest assigned by the loan capital, and the profit itself - the entrepreneurial income received by the lender, occurs under the influence of supply and demand in the loan capital market. Thus, interest expresses the relationship between the borrower and the lender and appears in the form of a certain interest rate.
Loan interest is, definition
Loan interest is a payment for the temporary use of the lent value. This is an economic category that operates on the basis of credit relations. It expresses the relationship between the borrower and the borrower, having their own specific interests in receiving and paying interest.
Unlike a loan, the loan interest does not imply a repayable, but an irrevocable distribution of the value of the produced goods, and not the entire value, but only the value of the surplus goods in its transformed form, profit. Interest is a direct deduction from the profit remaining at the disposal of the borrower. The amount of interest depends on the level of the interest rate and the amount loans received by the lender.
The formation of the lending policy of a commercial bank should be based on taking into account the following most important factors ":
Availability of capital;
The degree of riskiness and profitability of various types loans;
Stability of deposits;
General state of the economy states;
Impact on the economy of monetary and financial politicians;
Banking staff skills and experience;
Loan requirements of the district (region) served the bank.
These factors undoubtedly have an impact on the ongoing the bank loan interest rate policy.
Modern state with a market economy, controlling the movement of lending interest, can affect almost all parameters of social production. In particular, by raising the lending rate, through the Central Bank, it can contribute to monetary savings, lower prices and stabilize wages, increase production efficiency and increase the exchange rate of the national currency, reduce the competitiveness of its goods, increase the cost of exports and reduce the cost of imports of goods, increase import capital and containment exporting etc.
Deposit interest is, definition
Deposit interest is a payment of banks (credit institutions) for keeping money, securities and other material values in accounts, in depositories, vaults. It expresses the relationship of two participants in a credit transaction, and its content has two sides. The borrowers in the deposit operation are the clients of the bank (credit institution) - enterprises, organizations, institutions, other banks, the population, and as the borrower (borrower) - (the credit institution).
Level up interest rates on deposits (deposits) has not only economic value, but also social. In conditions of inflation, it is difficult to protect the interests of depositors, and therefore they are not interested in placing funds for long-term storage. Therefore, the deposit interest rate policy of banks should be linked to comprehensive customer service.
Interest rates on deposits in some countries depend on the amount of deposits: with their increase, the income on the deposit increases. In order to stimulate savings, especially for a long term, credit institutions of foreign countries pay fairly high interest rates to depositors (with taking into account low inflation), in particular, in the USA - from 5.7 to 9.8%, in Britain - from 3.0 to 11.2%, in Germany - from 2.5 to 5.2%, in France - from 4, 5 to 7.5%, in Italy - from 5.0 to 12.3%.
Interest calculation methods
In banking practice, there are various methods and ways of calculating interest.
Simple and compound interest is used.
Simple interest is, definition
Simple interest is accrual method, in which the amount of interest is determined throughout the entire period, based on the original amount of the debt, regardless of the amount periods accruals and their duration.
Simple interest is when the interest on the deposit is calculated at the end term... For example, open contribution for a year, with interest payment at the end of the deposit term.
The formula by which simple interest is calculated:
Compound interest is, the definition
Compound interest is method of calculating interest, in which accruals occur on the initial amount of the contribution (debt) and on the increase in the contribution (debt), i.e. the amount of interest accrued after the first accrual period. Thus, the base for calculating compound interest (as opposed to simple) will increase with each accrual period.
The compound interest formula looks like this:
interest rate is, definition
the interest rate is determined in accordance with the specific conditions for the use of loan capital and is subject to monetary and credit regulation by central bank... At the same time, the value of interest rates contributes either to the inflow of money capital from the money markets of other countries, or to its outflow.
Commercial banks set interest rates based on the discount rates adopted by the central banks of their countries. At the same time, large banks determine the minimum or best rates for loans to first-class borrowers.
Interests on deposits of bank clients are of great importance in the structure of interest rates. Interest paid by banks to their clients is always significantly lower than interest on loans (due to this difference, one of the main sources of bank profit is formed - interest margin)
Percentage margin is the definition
Used to replace non-ASCII characters in URI strings with codes like% D0% 9F% D1% 80% D0% BE (percent sign first, followed by a two-digit hexadecimal number).
In SQL, the percent sign for the LIKE command replaces any number of any characters, that is, it provides a mask search.
In Matlab programs, LaTeX markup and PostScript, the percent sign is used before the beginning of a line comment.
Calculators have a button with a percentage icon. Depending on the organization manufacturer's simplest calculators calculate.
What interest in mathematics? How to solve interest tasks? These questions emerge, alas, all of a sudden ... When a graduate reads the USE assignment. And they baffle him. But in vain. These are very simple concepts.
The only thing to remember is iron - what is one percent ... This concept is master key to solving problems with interest, and to working with interest in general.
One percent is one hundredth of a number ... And that's all. There is no more wisdom.
Reasonable question - and the hundredth part what date ? But the number referred to in the assignment. If it says about price, one percent is one hundredth of the price. Speaking of speed, one percent is one hundredth of the speed. Etc. It is clear that the number in question itself is always 100%. And if the number itself is not there, then the percentages do not make sense either ...
Another thing is that in complex problems the number itself will be hidden so much that you will not find it. But we are not yet aiming at the difficult. We deal with percent in mathematics.
I do not accentuate words for nothing one percent, one hundredth... Remembering what is one percent, you can easily find two percent, and thirty-four, and seventeen, and one hundred twenty-six! You will find as much as you need.
And this, by the way, is the main skill for solving problems with interest.
Let's try?
Let's find 3% of 400. First, find one percent... It will be one hundredth, i.e. 400/100 = 4. One percent is 4. And how many percent do we need? Three. So we multiply 4 by three. We get 12. That's it. Three percent of 400 is 12.
5% of 20 is 20 divided by 100 (one hundredth - 1%), and multiplied by five (5%):
5% of 20 will be 1. That's it.
It couldn't be easier. Let's quickly, before we forget, let's practice!
Find how much it will be:
5% from 200 rubles.
8% from 350 kilometers.
120% from 10 liters.
15% of 60 degrees.
4% of excellent students from 25 students.
10% of poor students out of 20 people.
Answers (in complete disarray): 9, 10, 2, 1, 28, 12.
These numbers are the number of rubles, degrees, students, etc. I didn’t write how many things, so that it was more interesting to decide ...
And if we need to write NS% from some number, for example, from 50? Yes, everything is the same. How much is one percent of 50? That's right, 50/100 = 0.5. And we have these percent - NS... Well, let's multiply 0.5 by NS! We get that NS% from 50 it is - 0.5x.
Hope it is interest in mathematics you get it. And you can easily find any number of percent of any number. It's simple. You are now capable of about 60% of all tasks for interest! More than half already. Well, are we finishing the rest? Okay, whatever you say!
In interest problems, the opposite situation is often encountered. We are given magnitudes (whatever), but you need to find interest ... We will also master this simple process.
3 people out of 120 - what is the percentage? Do not know? Well then let it be NS percent.
Let's calculate NS% from 120 people. In humans. We can do this. 120 divide by 100 (calculate 1%) and multiply by NS(calculate NS%). We get 1.2 NS.
Let's comprehend the result.
NS percent from 120 people, that's 1.2 NS human ... And we have three such people. It remains to equate:
1,2NS = 3
We solve this equation:
We remember that for the X we took the number of percent. So 3 people from 120 people is 2.5%.
That's all.
It can be done in another way. Get along with simple ingenuity, without any equations. We think how many times 3 people less than 120? Divide 120 by 3 and get 40. So 3 is 40 times less than 120.
The required number of people in percentage will be the same amount less than 100%. After all, 120 people is 100%. Divide 100 by 40, 100/40 = 2.5
That's all. Received 2.5%.
There is also a way of proportions, but this is, in essence, the same in an abbreviated form. All these methods are correct. As it is more convenient for you, it is more familiar, it is more understandable - consider so.
We train again.
Calculate how many percent are:
3 people out of 12.
10 rubles from 800.
4 textbooks from 160 books.
24 correct answers to 32 questions.
2 guessed answers to 32 questions.
9 hits out of 10 shots.
Answers (in disarray): 75%, 25%, 90%, 1.25%, 2.5%, 6.25%.
In the process of calculations, you may well come across fractions. Including inconvenient ones, such as 1.333333 ... And who told you to use the calculator? By yourself? Do not. Count without calculator as written in the "Fractions" topic. There are all kinds of interest ...
So we have mastered the transition from values to percentages and vice versa. You can take on the tasks.
One of the basic concepts of mathematics is percentage. In order to understand what a percentage is, it is enough to divide a given integer value by one hundred. One hundredth will be one percent (denoted 1%). As in the exact and economic sciences, and in other areas of life, percentages are used to indicate shares in relation to the whole. In this case, the whole itself is designated as 100%. In some cases, it is used when comparing two values: for example, sometimes the cost of goods is not compared in monetary units, but it is estimated by how many% the price of one product is more or less than the price of another. The term is also widely used in banking and in most cases is used synonymously with the phrase "interest rate".
The rule of finding percent of a number
Calculating percentages of a whole is one of the basic mathematical operations, and is also often used in everyday life. The rule for finding percentages of a number states that to solve such a problem, it must be multiplied by the% specified in the conditions, after which the result is divided by 100. You can also divide the number by 100, and multiply the result by the specified amount of%. It is important to remember one more thesis: if the percentage specified by the conditions exceeds 100%, then the resulting numerical value is always greater than the original (specified) - and vice versa.
The rule for finding a number by its percentage
There is a reverse rule for finding a number by its percentage. In order to get the result for such a mathematical operation (the second of the three basic types of problems for percentage calculations), it is necessary to divide the number indicated in the conditions by a given percentage value, and then multiply the result by 100. In this case, the first action calculates the number of units of the original value in 1 %, and the second - as a whole (that is, 100%). If the number of% exceeds 100, then the result obtained will always be less than the numerical value specified by the conditions of the problem - and vice versa.
The rule for finding the percentage of a number from another
The third basic type of mathematical problems for percentage calculations are those tasks in which it is necessary to use the rule for finding the percentage of a number from another (or the ratio of two quantities). It says that for the solution it is necessary to divide the second number by the first, and then multiply the result by one hundred. A similar ratio shows how much% one numerical value is from another (that is, in fact, we are talking about the ratio between two numerical values, expressed in%).
we see it quite often in everyday life. Take a bar of chocolate with a pack of ice cream that says "56% cocoa", "ice cream 100%." What is percentage?
Percentage called one hundredth part. Briefly write down 1 % ... Sign % replaces the word "percent".
Whatever number or value we take, its hundredth part is one percent of a given number or value. For example, for the number 400 (0.01 of the number 400), this is the number 4, therefore 4 is 1% of the number 400; 1 hryvnia (0.01 hryvnia) is 1 kopeck, therefore 1 kopeck is 1% of the hryvnia.
For example:
The puzzle contains 500 elements. How many elements are there in 1 percent of it? Let 500 puzzle pieces be 100%. Then 1% is 100 times less of its elements. Hence 500: 100 = 5 (el.). So 1% is 5 pieces of the puzzle.
Note: to find 1% of a number a, you need to divide this number by 100. Knowing which number or value is 1%, you can find a number or value that is a few percent.
For example:
Marina needs to sew a braid, 3 cm of which is 1% of its length. Marina sewed 50% of the braid. How many centimeters of the braid did she sew? Since 50% is 50 times more than 1%, Marina sewed braids 50 times larger than 3 cm. Hence 3.50 = 150 (cm). So, Marina sewed on 150 cm of braid.
In practice, it often happens that both of the above problems must be solved together - first, find what number or value falls on 1%, and then on a few percent. Such tasks are called tasks to find the percentage of the number.
For example:
Sweet pears contain 15% sugar. How much sugar is there in 3 kg of pears?
Let's make a short record of the task data.
Pears: 3 kg - 100%
Sugar: ? - 15%
1. How many kilograms corresponds to 1%?
Percentage of two numbers Is their ratio, expressed as a percentage. Percentage shows how many percent one number is from another.
interest
Income received from money invested in a bank or lent.
Remuneration calculated depending on the turnover, income.
Big Law Dictionary
interest
the subject of an obligation additional to a number of others (repayment of a loan, credit, unjustifiably received or saved, etc.), providing for the payment of sums of money upon the onset of a certain period; expressed in hundredths of the amount of the principal monetary obligation.
Interest
hundredths of a whole (taken as a unit). Percentage is called one hundredth and is indicated by a% sign; so, 19% of 3 m is 0.57 m, or 57 thousandth of a whole, that is, a tenth of a percent, has a special name ≈ ppm ≈ and a special designation 0/00. In economic and statistical calculations, as well as in many branches of science, it is customary to express parts of quantities in P .; to find them, the formula of simple percentages is used: if p% grows from a value over a year (or over some other period of time), then after t years it will turn into.
It is assumed that at the end of each year, the income for that year is withdrawn, so that for the new year the income is calculated from the original value (in this very sense, they speak of simple P.). If the income is counted to the original value and, therefore, the income for the new year is calculated from the accrued amount, then they speak of compound interest; in this case, the value into which a will turn in t years is calculated by the formula of complex P .:. When calculating P. for a part of the year, it is conventionally assumed that the year contains 360 days, and each month ≈ 30 days.
Complex metrics are used in many areas of economic activity and accounting (in banks, savings banks, etc.), as well as in various statistical calculations (primarily in determining the average annual rates of relative growth or decline over long periods of time (five years), decades, etc.).
Examples of the use of the word percentage in the literature.
The main arguments of the author boil down to the fact that American and Japanese statistics are reflected in different ways, for example, interest, paid on consumer loans, funds allocated for the purchase of real estate and its renovation, as well as many other factors and circumstances of a similar nature.
Taiwan in the 80s, loans for the development of export industries were issued under interest two times lower than the interbank rate and almost four times lower than the average loan price prevailing in the market.
Regulations interest are charged for the calendar number of days the debt is on the balance sheet, and the actual number of calendar days in a year is used in the calculations.
Specified what is in the accounting interest paid and received are reflected on the basis of the order of the structural unit of the accounting bank.
The Civil Code established the following procedure for the repayment of monetary debt: the amount of the payment made, which is insufficient to fulfill the monetary obligation in full, in the absence of another agreement, first of all repays the creditor's costs of obtaining the performance, then - interest, and in the remainder - the principal amount of the debt.
It shows how the colossal debts of third world countries, unemployment and environmental pollution, the production of weapons and the construction of nuclear power plants are linked to the mechanism that ensures the circulation of money: interest and complex interest.
Most people think they pay interest only when they take money on credit, and if the payment of interest is undesirable, it is enough just not to take money on credit.
So, if we eliminated interest and replaced them with a more perfect mechanism, then theoretically most of us would become at least twice as rich or we would need to work to maintain our current standard of living only half of the working time.
The trend is becoming clear - debts and interest on loans in the national economy are growing faster than income, which sooner or later should lead to a cap, even in highly developed countries.
I've always considered interest and complex interest like an invisible destruction machine that is working especially hard right now.
Instead of paying interest to those who have more money than they need, people - in order to return money into circulation, they would have to pay a small amount to remove money from circulation.
If today interest are an expression of private profit, then payment for the use of money would become an expression of public profit.
Although neutral money will not bring its owner interest however, they will maintain their stable value.
It doesn't matter how high or low the topical interest, goods and services can be sold much cheaper.
There is also a second question: what will happen if these people transfer their capital to other countries, where they can continue to receive interest instead of leaving them in their accounts, where, although they will retain their value, they will not bring interest?
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