Perhaps math wasn't your favorite subject in school, and numbers were scary and boring. But in adult life there is no escape from them. Without calculations, you can’t fill out a receipt for paying for electricity, you can’t draw up a business project, you can’t help your child with his homework. Often in these and other cases it is necessary to calculate the percentage of the amount. How to do this if you have vague memories of what percentage is from your school days? Let's strain our memory and figure it out.
Method one: percentage of the amount by determining the value of one percent
A percentage is one hundredth of a number and is denoted by the % sign. If you divide the amount by 100, you get just one percent. And then everything is simple. We multiply the resulting number by the required percentage. In this way it is easy to calculate the profit on a bank deposit.
For example, you deposited an amount of 30,000 at 9% per annum. What will be the profit? We divide the amount of 30,000 by 100. We get the value of one percent - 300. Multiply 300 by 9 and get 2,700 rubles - an increase to the original amount. If the contribution is for two or three years, then this figure doubles or triples. There are deposits for which interest payments are made monthly. Then you need to divide 2700 by 12 months. 225 rubles will be a monthly profit. If interest is capitalized (added to the total account), then the deposit amount will increase every month. This means that the percentage will be calculated not from the down payment, but from the new indicator. Therefore, at the end of the year you will receive a profit of not 2,700 rubles, but more. How many? Try to count.
Method two: convert percentages to decimals
As you remember, a percentage is a hundredth of a number. As a decimal it is 0.01 (zero point one hundredth). Therefore, 17% is 0.17 (zero point, seventeen hundredths), 45% is 0.45 (zero point, forty-five hundredths), etc. We multiply the resulting decimal fraction by the amount, the percentage of which is calculated. And we find the answer we are looking for.
For example, let's calculate the amount of income tax from a salary of 35,000 rubles. The tax is 13%. As a decimal it would be 0.13 (zero point one, thirteen hundredths). Let's multiply the amount of 35,000 by 0.13. It will turn out to be 4,550. This means that after deducting income tax, you will receive a salary of 35,000 - 4,550 = 30,050. Sometimes this amount, already without tax, is called “salary in hand” or “net.” In contrast, the amount together with tax is “dirty salary”. It is the “dirty salary” that is indicated in company vacancy announcements and in the employment contract. Less is given to your hands. How many? Now you can easily count.
Method three: count on a calculator
If you doubt your mathematical abilities, use a calculator. With its help, it is calculated faster and more accurately, especially when it comes to large amounts. It is easier to work with a calculator that has a button with a percentage sign. Multiply the amount by the percentage and press the % button. The required answer will be displayed on the screen.
For example, you want to calculate what your child care benefit will be for up to 1.5 years. It is 40% of average earnings for the last two closed calendar years. Let’s say the average salary is 30,000 rubles. On the calculator, multiply 30,000 by 40 and press the % button. Key = no need to touch. The answer 12,000 will be displayed on the screen. This will be the amount of the benefit.
As you can see, everything is very simple. Moreover, the “Calculator” application is now available on every cell phone. If the device does not have a special % button, then use one of the two methods described above. And perform multiplication and division on a calculator, which will facilitate and speed up your calculations.
Don't forget: there are online calculators to make calculations easier. They operate in the same way as regular ones, but are always at hand when you work on the computer.
Method four: making a proportion
You can calculate the percentage of the amount using a proportion. This is another scary word from a school mathematics course. Proportion is equality between two ratios of four quantities. For clarity, it is better to immediately understand it with a specific example. You want to buy boots for 8,000 rubles. The price tag indicates that they are sold at a 25% discount. How much is this in rubles? Of the 4 values, we know 3. There is a sum of 8,000, which is equal to 100%, and 25% that needs to be calculated. In mathematics, an unknown quantity is usually called X. The proportion we get is:
For ease of calculation, we convert percentages to decimal fractions. We get:
The proportion is solved as follows: X = 8,000 * 0.25: 1X = 2,000
2,000 rubles – discount on boots. We subtract this amount from the old price. 8,000 – 2,000= 6,000 rubles (new discounted price). This is such a nice proportion.
This method can also be used to determine the value of 100%, if you know the numerical indicator - say, 70%. At a company-wide meeting, the boss announced that 46,900 units of goods had been sold during the year, while the plan was only 70% fulfilled. How much did you need to sell to fully fulfill the plan? Let's make a proportion:
Converting percentages to decimal fractions, it turns out:
Let’s solve the proportion: X = 46,900 * 1: 0.7X = 67,000. These were the results of the work that the bosses expected.
As you may have guessed, the proportion method can be used to calculate what percentage a numerical indicator is of the amount. For example, while taking a test, you answered 132 out of 150 questions correctly. What percent of the task was completed?
There is no need to convert this proportion into decimal fractions; you can solve it right away.
X = 100 * 132: 150. As a result, X = 88%
As you can see, it's not all that scary. A little patience and attention, and now you have mastered the calculation of percentages.
A percentage is one hundredth of something. From the definition it follows that anything whole is taken as 100 percent. The percentage is indicated by the "%" sign.
How to solve problems in which you need to calculate percentages of a number? The percentage of a number can be calculated either by a formula or on a calculator.
- Example task: The price of a basket of apples is 160 rubles. The price of a basket of plums is 20% more expensive. How many rubles is more expensive than a basket of plums?
- Solution: In this task, we are required to do nothing more than find out how many rubles are 20% percent of the number 160.
Formula for calculating percentage:
1 way
Since 160 rubles is 100%, we first find out what 1% will be equal to. And then multiply this number by the 20% we need.
- 160 / 100 * 20 = 1,6 * 20 = 32
Answer: a basket of plums is 32 rubles more expensive.
Method 2
The second method is a modified version of the first method. Let's multiply the number that is 100% by a decimal fraction. This fraction is obtained by dividing the number of percentages that need to be found by 100. In our case:
- 20% / 100 = 0,2
We multiply 160 by 0.2 and get the same answer 32.
3 way
Method 3 - proportion.
Let's make a proportion of the form:
- x = 20%
- 160 = 100%
We multiply the parts of the proportion cross by cross and get the equation:
- x = (160 * 20) / 100
- x = 32
Calculating percentage of a number on a calculator
In order to calculate 20% of the number 160 on a calculator, you need:
- First, dial the number 160 on the screen - that is, our 100%
- Then press the multiply button "*"
- We will multiply by the number of percents that need to be found, that is, by 20. Press 20
- Now press the % key
- The answer should appear on the screen: 32
Read more about interest calculation algorithms in the article
It may be useful not only for high school students. In everyday life, this skill is necessary in order to calculate the loan payment, calculate and check whether the accountants correctly calculated the amount of taxation for you when you receive your salary. And for many employees of various companies and enterprises, this skill is simply necessary for work.
What is this - percentage? From the school curriculum, everyone remembers that a percentage in the world is considered to be a hundredth part of something. That is, to put it another way, the expression “3 percent” should be understood as 3 hundredths of any number. For the sake of brevity, people have adopted the symbol "%" for the word "percentage".
And from school, we all know how to calculate the percentage of divided by one hundred, finding the value of one percent, and then the resulting quotient is multiplied by a number indicating the number of percents that need to be found.
For example, you need to find out what 28% of 500 is. The line of reasoning should be as follows:
- Find the size of 1% of 500 by division.
- We find the given number by multiplying the resulting quotient from division by 100.
That is, 28% of 500 is 28/100 of 500. Another way to write this action is:
500 X 28/100 = 140.
Since numbers are not always easy to remember, and pen and paper are not always at hand, many people today use calculators.
To calculate, you can use the described method: divide the given number by one hundred and multiply by the required number of percent.
There is a faster calculation option:
- The specified number is entered into the calculator. In our case - 500.
- Next, press the “multiply” key.
- Then we type the number of the required percentages - for our version it is 28.
- Instead of equality, select the % sign on the calculator.
- We get the result - this is 140 in our example.
- In the cell that displays the calculated percentage, enter the equal sign “=”.
- Next, write down a given number from which you need to look for a percentage, or the “address” of the cell where this number has already been entered. In our example we will enter the number 500.
- The third step is to set the “multiply” or “*” sign.
- Now you should write down the number that reflects the amount of interest you are looking for. For us it's 28.
- The penultimate action will be to enter the “percentage” sign, which looks like “%”.
- To get the result, all you have to do is press the “Enter” button on your keyboard. The result - 140 - will immediately appear on the monitor.
Before starting to work in Excel, you should left-click to set the appropriate format in the table cells or use the “menu” function: “format - cells - number - percentage”.
For example, we are given the numbers 140 and 500. The question is posed this way: what percentage is 140 of 500?
- First, let's find what one percent of 500 is equal to. That is, we follow the old scheme and divide 500 by 100. We get 5.
- Now it remains to find out how many such percentages the given number 140 contains. To do this, 140 must be divided by 5. We get the same 28 percent!
- This calculation can be written in one formula as follows:
140: (500: 100) = 140: 500/100 = 140: 500 X 100 = 28.
That is, the number 140 out of 500 is 28 percent.
And in order to find out what percentage one number is of another, we should divide the smaller number by the larger one and multiply the quotient by 100.
These skills are extremely important for an entrepreneur who is engaged in trading. When setting prices for a product, it usually requires the ability to calculate the percentage of a number, since with the help of this action the necessary “markup” on the product is made. It is most convenient to mark up the entire assortment at the same percentage, for example, 15%.
But calculating net income requires another skill. For example, the daily revenue at the stall was 3,450 rubles. What is the net income from goods sold? Some novice entrepreneurs naively calculate 15% of gross revenue, and make a grave mistake! Having removed the “cheating” obtained in such an incorrect way from circulation, they then sit and puzzle over where the shortage came from.
And everything is very simple. After markup, the product began to contain not 100% of the cost, but 100% + 15% = 115%. Therefore, to find the amount of added value received, 15% is calculated as follows:
- They find 1% of the revenue by dividing it not by 100, but by 115. That is, in our case
- And now you can look for added value, which you can bravely extract from circulation.
These numbers are taken out of thin air, so you should not take these data seriously. But the calculation methods themselves deserve attention; there are no errors in them.
Each person is individual, and each formula may have errors. You need to choose the formula that will work for you.
Start with the average, or a formula approximating the average. If the results are not as effective as expected, try the following value: for weight loss - a lower value, for mass gain - a higher value.
Harris-Benedict equation
Basal metabolic rate according to the Harris-Benedict formula is determined taking into account gender, age and body size. The equation was first published in 1918. The formula is suitable for men and women over 18 years of age.
This formula has a fairly large error - according to the Academy of Nutrition and Dietetics, 90% agreement between the results and real data was recorded only in 60% of cases. That is, in 40% of situations the equation may show incorrect data, and mainly in the direction of increase. That is, as a result of the calculation, it may turn out that the need for calories is overestimated and a person begins to consume more calories than he actually needs.
New Harris-Benedict equation
Due to shortcomings of the basic Harris-Benedict formula, an updated equation was published in 1984. Rosa and Schizgal conducted a study on a larger group, with data taken from the research materials of Harris and Benedict in 1928-1935.
This formula already takes into account the features that in the old formula led to excess calories and therefore this formula was most often used to determine basal metabolism before 1990.
Mifflin Formula - St. George
Over time, people’s lifestyles change, new products appear, nutritional schedules and physical activity change. A new formula has been developed; it does not take into account the body's muscle mass, and is also calculated based on height, weight and age. This equation is used in clinical settings to determine calories based on basal metabolic rate.
According to research by the American Dietetic Association, the Mifflin-San Geor formula turned out to be the most accurate. In other sources it is considered. that this formula is 5% more accurate than the Harris-Benedict formula, but can still give a spread of +-10%. But this equation was only tested on Caucasian patients and therefore may not be accurate for other groups.
Ketch-McArdle formula
The formula was not developed based on weight, but rather on lean muscle mass. Thus, this formula ignores energy aimed at maintaining fat and its accuracy for obese people is lower than for athletic people.
If you are in good physical shape, the result of this equation will be quite accurate for you. If you have just set out on the path to improving your figure, use the Mifflin-San Geor formula.
WHO formula
The World Health Organization formula is based on the Schofield formula (gender, age, weight) taking into account height, which is currently used. Previously used in US dietary guidelines. Based on basal metabolic rate, thermic effect of food, physical activity and thermoregulation.
Based on body area
The formula is suitable for people over 20 years of age. Energy expenditure (or metabolic rate) at rest is proportional to body surface area, usually expressed in kcal per square meter of body surface area per hour (kcal/m2/m). Body surface area can be calculated based on your height and weight.
Calorie calculation
Why do you need to calculate the number of calories per day?
The answer is simple - in order to maintain, gain or lose weight, you need to know how many calories your body consumes. If you want to lose weight, you need to burn more calories than you consume. You only get calories if you eat or drink something. And you have to constantly spend calories - on the work of the body itself, on physical and mental stress.
Average number of calories per day
In general, women require 1500-2000 calories to maintain weight. For men, this value is higher - 2000-2500 calories.
How many calories do you need to lose weight or gain weight?
Using an online calculator, you can calculate the calorie needs that you need for your existence, and calculate the number of calories for losing weight, gaining or maintaining weight. Calories are calculated based on weight, height, age and activity. Based on the data received and your desired weight, the calculator will calculate the number of calories you should consume per day to lose, gain or maintain weight. As a rule, calculations are made using several methods that will show an approximate range. This is done to minimize the error of each individual calculation method.
Minimum calories per day for weight loss
The calculation of the number of calories is shown in the “Weight loss” column. "Extreme Weight Loss" will show you the minimum possible calorie values for reference, but it is not recommended to use them. If you reduce your calorie intake below the minimum, your body will begin to burn not only fat, but also muscle to obtain energy. The metabolic rate will drop and even a slight excess of calories will be stored by the body. In addition, muscles consume several times more energy than fat cells. Therefore, burning muscles does not lead to positive results.
Zigzag calories
The calculation results contain a table for calculating calories by day, the so-called “zigzag”. It is believed that the best results are obtained if you vary your daily caloric intake slightly, maintaining an average value.
How to count kilocalories
A kilocalorie is a thousand calories. One calorie is how much energy is required to heat 1 ml of water by 1 degree. But there is also a food or dietary calorie, which is equal to a kilocalorie. Product packaging may indicate the calorie content of foods as either “kkak” or “cal”, and this will be referred to as kilocalories.
Calorie calculation example
Anna, office worker, two children. Does household chores when not at work. He goes in for sports three times a week. Height 163 cm, weight 65 kg, age 35 years. Wants to reduce weight to 57 kg. According to the Mifflin-San Jeor formula, the daily calorie consumption will be 1833 kcal, on average 1918. To lose weight, Anna needs to reduce her daily calorie intake by about 500 calories per day, that is, consume 1400 kcal.
Should you eat the same amount of calories?
You can stick to the same number of calories per day, or you can move 200-500 calories to the previous or subsequent day from the day of training. Also, if your weight suddenly stops (weight plateau), then consuming calories according to the Zigzag pattern will help move it off the ground.
Is it possible to lose weight only on a diet?
You can lose weight, but when you reduce your daily caloric intake, a person loses not only fat, but also muscle. Try to lead a more active lifestyle, do exercises, add small physical activities
Weight loss rate
Weight gain rate
The ideal amount for increasing muscle mass is 1 kg per month for men and 0.5 kg per month for women. A large increase will lead to an increase not only in muscle, but also in fat.
Should I drink water?
Drinking clean water is necessary when losing weight.
Warning
All calculations are based on mathematical and statistical formulas. But only a doctor can give an accurate assessment and recommendations. Please consult your physician before starting a diet or changing your exercise level.
The very concept of interest must be familiar to many, but for some reason difficulties arise in the calculations associated with it. And such problems happen not only to small children, but even to mature adults. Someone might argue that he doesn’t need interest in his life, since he doesn’t encounter it anywhere. But this is absolutely not true. All tax rates, including income tax (NDFL), VAT, etc. are calculated as a certain established percentage of the number. The same situation applies to loans, which most citizens use. That is why you need to know how to calculate percentages correctly, so as not to be deceived in the modern world.
General case of calculation
- 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 cost of goods. It is said that the price of the product 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.
- We determine 20% of 300: 3 rubles. * 20% = 60 rub.
Now someone who understands the issue may be surprised and ask why such difficulties, because you can do it completely differently: 300 * 0.2 = 60 rubles. This is possible, but for some reason not everyone understands that first you need to convert the value in “%” into a coefficient, and then multiply the number by it. They do everything as it is convenient for him and as they were taught at school. Both options are valid.
But a completely different situation may arise: it will be necessary to determine what percentage a certain value is of a certain amount. In this case, the calculation algorithm is completely different:
- It is again necessary to find 1% of a known number by dividing by 100%.
- Then you will need to divide the desired number by the resulting number.
As an example, we give the opposite situation. It is known that VAT is 60 rubles. The price of the product is 300 rubles. What is the value added tax rate?
Calculation:
- Let's find the same 1%, it will be 3 UAH..
- Divide 60 by 3 and 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.
Calculating interest 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. Let's remember the well-known X. In order to recall the rule of proportion, let's give an example: an employee is paid a salary of 10,000 rubles, the personal income tax rate is 15%. It is necessary to determine how much a person will actually receive on the 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 withheld from the employee. Therefore, the salary to be paid will be 10,000 – 1500 = 8500 rubles.
Calculation in Excel
It is difficult to find a modern person who does not use software. And one of these frequently used programs is excel. In order to calculate interest 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 makes up of the total number, then you need to enter the value in the cell after the “=” sign: Particular/General. There is no need to divide or multiply by 100; you just need to set the percentage format of the number for the cell where the calculation is being carried out. In this case, instead of indicators in Excel itself, the formula will contain the names 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 income item occupies in the total income. In this case, the formula in Excel will look similar, with the quotient in the numerator and the general in the denominators, only the denominator itself will be permanently fixed. This is easy to do using the $ icon. The formula looks like: 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 have a completely different form:
- 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 one)/Value of the previous period.
Loan rate: calculation options
When also considering the question of how interest is calculated, one cannot fail to mention the lending rate. This is the most common practical method when people begin to calculate this value using mathematical techniques.
For some reason, many people think that performing mathematical operations is quite simple. 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 - this is the fee for the year of using the loan. If we divide by 12 months, we get the monthly overpayment amount for the loan.
But in reality, the calculation algorithm is completely different. It all depends on which calculation method is used, on how the rate is calculated - every day, monthly or annually. And then we’ll talk in more detail about credit calculations.
Loans are calculated using an annuity and differentiated system
Differentiated calculation system
This is a beneficial system for the borrower himself, since it allows him to save on the amount of overpayment. Why is this 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 outstanding loans. This scheme is characterized by the fact that first the borrower pays the maximum allowable payments, and only then the smallest ones.
In this case, both simple and compound interest formulas can be used. The only difference is when and with what frequency they are accrued.
Let us 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 upon completion 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 can be in days, months, quarters (it all depends on the period for which the overpayment is accrued);
- Ty- the number of periods per year that are used in the calculation. This could 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 monthly accrual. We get the following calculation: amount to be refunded = 1000*(1+0.1*(10/12)) = 1083 rubles. The client will pay 81 rubles for using credit funds.
The calculation of such a plan is used mainly 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 this technique is quite complex; 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 penalties, fines, and obligatory payments for the month is added to the principal amount of the debt and a rate is charged on it.
Calculation of capitalization of interest on deposits
When talking about this method, special attention must be paid to capitalization. It is when calculating it that you can learn how to calculate interest on interest. 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, interest on a deposit is paid to the client once a year, and only if at the end of the year he does not withdraw it, will it be automatically credited to the deposit. And already in the second year, profit will be accrued on the total amount. The following formula is used for this:
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, let’s again give a clear example: a bank client decided 10,000 rubles. place it on deposit at 12% per annum. Capitalization is monthly, and the deposit period is one year.
The calculation will be as follows: 10000 * (1+0.12/12)*12 = 11268.
This means that the client, along with his deposit, will be able to receive 11,268 rubles after withdrawing the entire amount from the account. In this case, the net profit will be 1268 rubles. (11268-10000).
If we consider two calculation schemes, then for those who invest in a deposit account, a complex method is more profitable, since frequent capitalization allows one to increase the basis for calculation. The simple method is more convenient for loans. But the choice is still up to the bank, not the borrower or client.
Annuity scheme
Regarding , there is no fundamental difference in the calculation method: either a simple or complex formula can be used. The bottom line is that the amount of interest and the principal amount of the debt is distributed in equal parts. Repayment is made monthly.
But to be honest, borrowers themselves very rarely use these formulas, since every bank website and just on the Internet has a loan calculator where you can enter data and easily and quickly get the desired result.
Thus, at first glance it seems that calculating interest is not necessary for everyday life and many do not pay attention to this point. But in order to be economically literate and choose the most profitable options, you need to know this.
