20 percent of 120. How to subtract percentages from a number: three effective ways

A percentage is a hundredth of a number. This mathematical concept is widely used in everyday life: percentages indicate statistical data, the composition of food and various materials, as well as interest rates on loans and deposits.

Percentages allow you to compare parts of a whole with each other, greatly simplifying calculations. Calculating percentages can be done in your head or on paper, using a formula, or using a calculator or Excel program.

Quick navigation through the article

• Divide the number from which you need to find the percentage by 100;
• Multiply the result obtained by the desired percentage.

For convenience, the number can be multiplied by percentages written as a decimal fraction (divide by one hundred). For example, to find 20% of 50, you need 50/100*20=10 or 50*0.2=10.

Calculation on a calculator

You can use a calculator to calculate percentages. To do this you will need:

• Enter the required number;
• Click the “Multiply” button;
• Specify the number of percentages;
• Press the "%" key.

If a regular calculator is not available, you can use the Calculator program in operating system Windows (go to “Start”, “Accessories”, “Calculator”). There are also many online calculators that require internet access to use.

Excel

Interest calculations can be performed in Microsoft Office Excel. To do this you need:

• Open the program;
• In any cell, enter the number from which you want to find the percentage;
• Place the “=” sign in the cell in which the result will be displayed;
• Select cell with specified number, enter the “*” sign, enter percentages, put the “%” sign and press the “Enter” button;
• The second cell will display the result of the calculations.

You can enter numbers into any cells of the file (on the same sheet or on different ones).

Percentage

There are calculations that allow you to determine what percentage one number is of another. For this calculation you will need:

• The number whose percentage needs to be found must be multiplied by 100;
• Divide the result by the number from which the percentage is calculated.

For example, in order to find what percentage 50 is of 200, you need 50*100/200=25 (50 is 25 percent of 200).

Finding a number by percentage

• Divide the given number by the percentage;
• Multiply the result by 100.

For example, to find a number whose 25% is 50, you will need 50/25*100=200.

The quotient of two numbers is called the ratio of these numbers.

Let's look at examples of how to find the ratio of two numbers.

4 And 20

Number 4 amounts to 20% from the number 20 . To calculate, we divide 4 on 20 and multiply by 100 , we get 4 20 × 100 = 20%

Number 20 amounts to 500% from the number 4 . To calculate, we divide 20 on 4 and multiply by 100 , we get 20 4 × 100 = 500%

From the number 4 we get 20 increasing by 400% . To calculate, we divide 20 on 4 , multiply by 100 and take away 100% , we get 20 4 × 100 – 100 = 400%

From the number 20 we get 4 reducing the number by 80% . To calculate, we divide 4 on 20 , multiply by 100 and take away 100% , we get 4 20 × 100 – 100 = -80%. If the result is a negative value, then the number must be reduced, if positive, then increased.

Let's find the ratio of two real numbers.

Example Let's find the ratio of numbers 0.3 And 0.6

Number 0.3 amounts to 50% from the number 0.6 . To calculate, we divide 0.3 on 0.6 and multiply by 100 , we get 0.3 0.6 × 100 = 50%

Number 0.6 amounts to 200% from the number 0.3 .

How to calculate the percentage of the amount?

To calculate, we divide 0.6 on 0.3 and multiply by 100 , we get 0.6 0.3 × 100 = 200%

From the number 0.3 we get 0.6 increasing by 100% . To calculate, we divide 0.6 on 0.3 , multiply by 100 and take away 100 , we get 0.6 0.3 × 100 – 100 = 100%

From the number 0.6 we get 0.3 reducing the number by 50% . To calculate, we divide 0.3 on 0.6 , multiply by 100 and take away 100 , we get 0.3 0.6 × 100 – 100 = -50%.

How to calculate (calculate) the percentage of the amount?

One percent- this is one hundredth. The word itself percent comes from the Latin "pro centum", meaning "hundredth part".

1.

Interest calculator

Formula for calculating percentage share.

Let two numbers be given: A 1 and A 2. It is necessary to determine what percentage of the number A 1 is from A 2.

P = A 1 / A 2 * 100.

Download the convenient style="color:red"> calculator - any calculations,
percentages, calculation using formulas, recording and printing results

2. Formula for calculating percentage of a number.

Let the number A 2 be given. It is necessary to calculate the number A 1, which is a given percentage P of A 2.

A 1 = A 2 * P / 100.

3. Formula for increasing a number by a given percentage. Value with VAT.

Let the number A 1 be given. We need to calculate the number A 2, which is greater than the number A 1 by a given percentage P. Using the formula for calculating the percentage of a number, we get:

A 2 = A 1 + A 1 * P / 100.

A 2 = A 1 * (1 + P / 100).

Note. Our ClasCalc calculator has a special “adding percentage” operation, which is denoted +% .

4. Formula for reducing a number by a given percentage.

Let the number A 1 be given. We need to calculate the number A 2, which is less than the number A 1 by a given percentage P. Using the formula for calculating the percentage of a number, we get:

A 2 = A 1 - A 1 * P / 100.

A 2 = A 1 * (1 - P / 100).

5. Formula for calculating the initial amount. Price without VAT.

Let a number A 1 be given, equal to some initial number A 2 with an added percentage P. We need to calculate the number A 2 . In other words: we know the monetary amount including VAT, we need to calculate the amount excluding VAT. Let us denote p = P / 100, then:

A 1 = A 2 + p * A 2 .

A 1 = A 2 * (1 + p).

A 2 = A 1 / (1 + p).

See VAT calculation formulas, amount with VAT, amount without VAT, allocation of VAT

6. Calculation of interest on a bank deposit. Formula for calculating simple interest.

If interest on a deposit is accrued once at the end of the deposit term, then the amount of interest is calculated using the formula simple interest.

S = K + (K*P*d/D)/100
Sp = (K*P*d/D)/100

Where:
S is the amount of the bank deposit with interest,
Sp - amount of interest (income),
K— initial amount(capital),
d — number of days of accrual of interest on the attracted deposit,
D is the number of days in a calendar year (365 or 366).

7. Calculation of interest on a bank deposit when calculating interest on interest. Formula for calculating compound interest.

If interest on a deposit is accrued several times at equal intervals and is credited to the deposit, then the amount of the deposit with interest is calculated using the formula compound interest.

S = K * (1 + P*d/D/100) N

Where:

P—annual interest rate,

When calculating compound interest, it is easier to calculate total amount with interest, and then calculate the amount of interest (income):

Sp = S - K = K * (1 + P*d/D/100) N - K

Sp = K * ((1 + P*d/D/100) N - 1)

To determine what is more profitable - a deposit under higher percentage accrued according to the simple interest formula or a deposit at a lower interest, but accrued according to the compound interest formula, see

Formulas for calculating compound interest and choosing a deposit.

8. Another compound interest formula.

If the interest rate is not given on an annual basis, but directly for the accrual period, then the compound interest formula looks like this.

S = K * (1 + P/100) N

Where:
S—deposit amount with interest,
K - deposit amount (capital),
P - interest rate,
N is the number of interest periods.

More details and examples of calculating interest using simple and compound interest formulas.

For example, calculate what percentage the number 52 is from the number 400.

According to the rule: 52: 400 * 100 - 13 (%).

Typically, such relationships are found in tasks when quantities are given, and it is necessary to determine by what percentage the second quantity is greater or less than the first (in the task question: by how many percent did they exceed the task; by what percent did they complete the work; by what percent did the price decrease or increase, etc. .

How to find the percentage of a number

Solving problems involving the percentage ratio of two numbers rarely involves only one action. Most often, solving such problems consists of 2-3 actions.

Examples.

1. The plant was supposed to produce 1,200 products in a month, but produced 2,300 products. By what percentage did the plant exceed the plan?

1st option
Solution:
1,200 products is the plant plan, or 100% of the plan.
1) How many products did the plant produce above plan?
2,300 – 1,200 = 1,100 (ed.)

2) What percentage of the plan will be above-plan products?
1,100 from 1,200 => 1,100: 1,200 * 100 = 91.7 (%).

2nd option
Solution:
1) What percentage is the actual production of products compared to the planned one?
2,300 from 1,200 => 2,300: 1,200 * 100 = 191.7 (%).

2) By what percentage was the plan exceeded?
191,7 — 100 = 91,7 (%)
Answer: 91.7%.

2. Wheat yield on the farm for last year amounted to 42 c/ha and was included in the next year’s plan. The following year, the yield dropped to 39 c/ha. To what percentage was the next year's plan fulfilled?

1st option
Solution:

42 c/ha is the farm plan for this year, or 100% of the plan.

1) How much has the yield decreased compared to
with a plan?
42 – 39 = 3 (c/ha)

2) By what percentage was the plan not completed?
3 of 42 => 3: 42 * 100 = 7.1 (%).

3) How much of this year’s plan has been fulfilled?

100 — 7,1 = 92,9 (%)

2nd option
Solution:
1) What percentage is the yield of this goal compared to the plan?
39 from 42 39: 42 100 - 92.9 (%).
Answer: 92.9%.

One percent is a hundredth of a number. This concept used when you need to indicate the ratio of a part to the whole. In addition, several values ​​can be compared as percentages, but be sure to indicate relative to which integer the percentages are calculated. For example, expenses are 10% higher than income or the price of train tickets has increased by 15% compared to last year's tariffs. A percent number above 100 means that the proportion is greater than the whole, as is often the case in statistical calculations.

Percentage as financial concept- payment from the borrower to the lender for providing money for temporary use. In business, the expression “work for interest” is common. In this case, it is understood that the amount of remuneration depends on profit or turnover (commissions). It is impossible to do without calculating percentages in accounting, business, banking. To simplify calculations, an online interest calculator has been developed.

The calculator allows you to calculate:

• Percentage of the set value.
• Percentage of the amount (tax on actual salary).
• Percentage of the difference (VAT from ).
• And much more...

When solving problems using a percentage calculator, you need to operate with three values, one of which is unknown (a variable is calculated using the given parameters). The calculation scenario should be selected based on the specified conditions.

Examples of calculations

1. Calculating the percentage of a number

To find a number that is 25% of 1,000 rubles, you need:

• 1,000 × 25 / 100 = 250 rub.
• Or 1,000 × 0.25 = 250 rubles.

To calculate using a regular calculator, you need to multiply 1,000 by 25 and press the % button.

2. Definition of an integer (100%)

We know that 250 rub. is 25% of a certain number. How to calculate it?

Let's make a simple proportion:

• 250 rub. - 25%
• Y rub. - 100 %
• Y = 250 × 100 / 25 = 1,000 rub.

3. Percentage between two numbers

Let's say a profit of 800 rubles was expected, but we received 1,040 rubles. What is the percentage of excess?

The proportion will be like this:

• 800 rub. - 100 %
• RUB 1,040 – Y%
• Y = 1,040 × 100 / 800 = 130%

Exceeding the profit plan is 30%, that is, fulfillment is 130%.

4. Calculation is not based on 100%

For example, a store consisting of three departments receives 100% of customers. In the grocery department - 800 people (67%), in the household chemicals department - 55. What percentage of customers come to the household chemicals department?

Proportion:

• 800 visitors – 67%
• 55 visitors - Y%
• Y = 55 × 67 / 800 = 4.6%

5. By what percentage is one number less than another?

The price of the product dropped from 2,000 to 1,200 rubles. By what percentage did the price of the product fall or by what percentage did 1,200 less than 2,000?

• 2 000 - 100 %
• 1,200 – Y%
• Y = 1,200 × 100 / 2,000 = 60% (60% to the figure 1,200 from 2,000)
• 100% − 60% = 40% (the number 1,200 is 40% less than 2,000)

6. By what percentage is one number greater than another?

The salary increased from 5,000 to 7,500 rubles. By what percentage did the salary increase? What percentage is 7,500 greater than 5,000?

• 5,000 rub. - 100 %
• 7,500 rub. - Y%
• Y = 7,500 × 100 / 5,000 = 150% (in numbers 7,500 is 150% of 5,000)
• 150% − 100% = 50% (the number 7,500 is 50% greater than 5,000)

7. Increase the number by a certain percentage

The price of product S is above 1,000 rubles. by 27%. What is the price of the product?

• 1,000 rub. - 100 %
• S - 100% + 27%
• S = 1,000 × (100 + 27) / 100 = 1,270 rub.

The online calculator makes calculations much simpler: you need to select the type of calculation, enter the number and percentage (in the case of calculating a percentage, the second number), indicate the accuracy of the calculation and give the command to begin the action.

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 "%" symbol.

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:

1. First, dial the number 160 on the screen - that is, our 100%
2. Then press the multiply button "*"
3. We will multiply by the number of percents that need to be found, that is, by 20. Press 20
4. Now press the % key
5. The answer should appear on the screen: 32

Read more about interest calculation algorithms in the article

In life, sooner or later everyone will be faced with a situation where it will be necessary to work with percentages. But, unfortunately, most people are not prepared for such situations. AND this action causes difficulties. This article will tell you how to subtract percentages from a number. Moreover, they will be dismantled various ways solving a problem: from the simplest (using programs) to one of the most complex (using a pen and paper).

We subtract manually

Now we will learn how to subtract with a pen and paper. The actions that will be presented below are studied by absolutely every person in school. But for some reason, not everyone remembered all the manipulations. So, we have already figured out what you will need. Now we'll tell you what needs to be done. To make it more clear, we will consider an example, taking specific numbers as a basis. Let's say you want to subtract 10 percent from the number 1000. Of course, it is quite possible to do these actions in your head, since the task is very simple. The main thing is to understand the very essence of the decision.

First of all, you need to write down the proportion. Let's say you have two columns with two rows. You need to remember one thing: numbers are entered in the left column, and percentages are entered in the right column. Two values ​​will be written in the left column - 1000 and X. X is included because it symbolizes the number that will need to be found. In the right column will be entered - 100% and 10%.

Now it turns out that 100% is the number 1000, and 10% is X. To find x, you need to multiply 1000 by 10. Divide the resulting value by 100. Remember: the required percentage must always be multiplied by the taken number, after which the product should be divided by 100%. The formula looks like this: (1000*10)/100. The picture will clearly show all the formulas for working with percentages.

We got the number 100. This is what lies under that X. Now all that remains to be done is subtract 100 from 1000. It turns out 900. That's all. Now you know how to subtract percentages from a number using a pen and notebook. Practice on your own. And over time, you will be able to perform these actions in your mind. Well, we move on, talking about other methods.

Subtract using the Windows calculator

It’s clear: if you have a computer at hand, then few people will want to use a pen and notebook for calculations. It's easier to use technology. That’s why we’ll now look at how to subtract percentages from a number using a Windows calculator. However, it is worth making a small note: many calculators are capable of performing these actions. But the example will be shown using a Windows calculator for greater understanding.

Everything is simple here. And it is very strange that few people know how to subtract percentages from a number in a calculator. Initially, open the program itself. To do this, go to the Start menu. Next, select "All Programs", then go to the "Accessories" folder and select "Calculator".

Now everything is ready to start solving. We will operate with the same numbers. We have 1000. And we need to subtract 10% from it. All you need to do is enter the first number (1000) into the calculator, then press minus (-), and then click on percentage (%). Once you have done this, you will immediately see the expression 1000-100. That is, the calculator automatically calculated how much 10% of 1000 is.

Now press Enter or equals (=). Answer: 900. As you can see, both the first and second methods led to the same result. Therefore, it’s up to you to decide which method to use. Well, in the meantime we move on to the third and final option.

Subtract in Excel

Many people use Excel. And there are situations when it is vital to quickly make calculations in this program. That is why now we will figure out how to subtract a percentage from a number in Excel. This is very easy to do in the program using formulas. For example, you have a column with values. And you need to subtract 25% from them. To do this, select the column next to it and enter equal (=) in the formula field. After that, click LMB on the cell with the number, then put “-” (and again click on the cell with the number, after that enter - “*25%). You should get something like in the picture.

As you can see, this is the same formula as given the first time. After pressing Enter you will receive the answer. To quickly subtract 25% from all numbers in a column, just hover over the answer, placing it in the lower right corner, and drag down the required number of cells. Now you know how to subtract a percentage from a number in Excel.

Conclusion

Finally, I would like to say only one thing: as you can see from all of the above, in all cases only one formula is used - (x*y)/100. And it was with her help that we were able to solve the problem in all three ways.

Interest is one of the concepts of applied mathematics that are often encountered in everyday life. Thus, you can often read or hear that, for example, 56.3% of voters took part in the elections, the rating of the winner of the competition is 74%, industrial production increased by 3.2%, the bank charges 8% per annum, milk contains 1.5% fat, fabric contains 100% cotton, etc. It is clear that understanding such information is necessary in modern society.

One percent of any value - sum of money, number of school students, etc. - one hundredth of it is called.
The percentage is denoted by the % sign. Thus,

1% is 0.01, or \(\frac(1)(100)\) part of the value
Here are some examples:
- 1% of the minimum wage 2300 rub. (September 2007) - this is 2300/100 = 23 rubles;
- 1% of the population of Russia, equal to approximately 145 million people (2007), is 1.45 million people;

- A 3% concentration of a salt solution is 3 g of salt in 100 g of solution (recall that the concentration of a solution is the part that is the mass of the dissolved substance from the mass of the entire solution).

The word "percent" comes from the Latin pro centum, meaning "from a hundred" or "per 100." This phrase can also be found in modern speech. For example, they say: “Out of every 100 lottery participants, 7 participants received prizes.” If we take this expression literally, then this statement is, of course, false: it is clear that it is possible to select 100 people who participated in the lottery and did not receive prizes. In fact, the exact meaning of this expression is that 7% of lottery participants received prizes, and this understanding corresponds to the origin of the word "percentage": 7% is 7 out of 100, 7 people out of 100 people.

The "%" sign became widespread at the end of the 17th century. In 1685, the book “Manual of Commercial Arithmetic” by Mathieu de la Porte was published in Paris. In one place it was about percentage, which was then designated “cto” (short for cento). However, the typesetter mistook this “s/o” for a fraction and printed “%”. So, due to a typo, this sign came into use.

Any number of percentages can be written as a decimal fraction expressing a fraction of a quantity.

To express percentages as numbers, you need to divide the number of percentages by 100. For example:

For a reverse transition, the reverse action is performed. Thus, To express a number as a percentage, you need to multiply it by 100:

In practical life, it is useful to understand the relationship between the simplest percentage values ​​and the corresponding fractions: half - 50%, a quarter - 25%, three quarters - 75%, a fifth - 20%, three fifths - 60%, etc.

It is also useful to understand the different forms of expressing the same change in quantity, formulated without percentages and using percentages. For example, in messages "Minimum wage increased by 50% since February" and "The minimum wage has been increased by 1.5 times since February" say the same thing. In the same way, to increase by 2 times means to increase by 100%, to increase by 3 times means increase by 200%, decrease by 2 times - this means decrease by 50%.

Likewise
- increase by 300% - this means increase 4 times,
- reduce by 80% - this means reduce by 5 times.

Percentage problems

Since percentages can be expressed as fractions, percent problems are essentially the same as fraction problems. In the simplest problems involving percentages, a certain value a is taken as 100% (“whole”), and its part b is expressed by the number p%.

Depending on what is unknown - a, b or p, there are three types of problems involving percentages. These problems are solved in the same way as the corresponding fraction problems, but before solving them, the number p% is expressed as a fraction.

1. Finding the percentage of a number.
To find \(\frac(p)(100)\) from a, you need to multiply a by \(\frac(p)(100)\):

So, to find p% of a number, you need to multiply this number by the fraction \(\frac(p)(100)\). For example, 20% of 45 kg is equal to 45 0.2 = 9 kg, and 118% of x is equal to 1.18x

2. Finding a number by its percentage.
To find a number from its part b, expressed as the fraction \(\frac(p)(100) , \; (p \neq 0) \), you need to divide b by \(\frac(p)(100) \):
\(a = b: \frac(p)(100)\)

3. Finding the percentage ratio of two numbers.
To find what percentage the number b is of a \((a \neq 0) \), you must first find out what part b is of a, and then express this part as a percentage:

The quotient of two numbers expressed as a percentage is called percentage these numbers. Therefore the last rule is called rule for finding the percentage ratio of two numbers.

It is easy to see that the formulas

Compound problems involving percentages are solved similarly to problems involving fractions.

Simple percentage growth

When a person does not pay his rent on time, he is subject to a fine called a “penalty” (from the Latin roena - punishment). So, if the penalty is 0.1% of the rent amount for each day of delay, then, for example, for 19 days of delay the amount will be 1.9% of the rent amount. Therefore, together with, say, 1000 rubles. rent, a person will have to pay a penalty of 1000 0.019 = 19 rubles, and a total of 1019 rubles.

It is clear that in different cities and different people the rent, the amount of penalties and the time of delay are different. Therefore, it makes sense to create a general rent formula for sloppy payers, applicable under all circumstances.

Let S be the monthly rent, the penalty is p% of the rent for each day of delay, and n is the number of days overdue. The amount that a person must pay after n days of delay will be denoted by S n.
Then for n days of delay the penalty will be pn% of S, or \(\frac(pn)(100)S\), and in total you will have to pay \(S + \frac(pn)(100)S = \left(1+ \frac(pn)(100) \right) S\)
Thus:
\(S_n = \left(1+ \frac(pn)(100) \right) S \)

This formula describes many specific situations and has a special name: simple percentage growth formula.

A similar formula will be obtained if a certain value decreases over a given period of time by a certain number of percent. As above, it is easy to verify that in this case
\(S_n = \left(1- \frac(pn)(100) \right) S \)

This formula is also called simple percentage growth formula although the given value actually decreases. Growth in this case is “negative”.

Compound interest growth

In Russian banks for some types of deposits (the so-called time deposits, which cannot be taken earlier than after a period specified in the contract, for example, in a year) is accepted next system income payments: for the first year that the deposited amount is in the account, the income is, for example, 10% of it. At the end of the year, the depositor can withdraw from the bank the money invested and the income earned - "interest", as it is usually called.

If the depositor has not done this, then the interest is added to the initial deposit (capitalized), and therefore at the end of the next year 10% is added by the bank to the new, increased amount. In other words, with such a system, “interest on interest” is calculated, or, as they are usually called, compound interest.

Let's calculate how much money the investor will receive in 3 years if he deposited 1000 rubles into a fixed-term bank account. and will never take money from the account for three years.

10% from 1000 rub. are 0.1 1000 = 100 rubles, therefore, in a year his account will have
1000 + 100 = 1100 (r.)

10% of the new amount 1100 rub. are 0.1 1100 = 110 rubles, therefore, after 2 years there will be
1100 + 110 = 1210 (r.)

10% of the new amount 1210 rub. are 0.1 1210 = 121 rubles, therefore, after 3 years there will be
1210 + 121 = 1331 (r.)

It is not difficult to imagine how much time, with such a direct, “head-on” calculation, it would take to find the amount of the deposit after 20 years. Meanwhile, the calculation can be done much easier.

Namely, in a year the initial amount will increase by 10%, that is, it will be 110% of the initial one, or, in other words, it will increase by 1.1 times. Next year the new, already increased amount will also increase by the same 10%. Therefore, after 2 years the initial amount will increase by 1.1 1.1 = 1.1 2 times.

In another year, this amount will increase by 1.1 times, so the initial amount will increase by 1.1 1.1 2 = 1.1 3 times. With this method of reasoning, we obtain a much simpler solution to our problem: 1.1 3 1000 = 1.331 1000 - 1331 (r.)

Let us now solve this problem in general view. Let the bank accrue income in the amount of p% per annum, the deposited amount is equal to S rub., and the amount that will be in the account in n years is equal to S n rub.

The value p% of S is \(\frac(p)(100)S \) rub., and after a year the amount will be in the account
\(S_1 = S+ \frac(p)(100)S = \left(1+ \frac(p)(100) \right)S \)
that is, the initial amount will increase by \(1+ \frac(p)(100)\) times.

Over the next year, the amount S 1 will increase by the same amount, and therefore in two years the account will have the amount
\(S_2 = \left(1+ \frac(p)(100) \right)S_1 = \left(1+ \frac(p)(100) \right) \left(1+ \frac(p)(100) ) \right)S = \left(1+ \frac(p)(100) \right)^2 S \)

Similarly \(S_3 = \left(1+ \frac(p)(100) \right)^3 S \), etc. In other words, the equality
\(S_n = \left(1+ \frac(p)(100) \right)^n S \)

This formula is called compound interest formula, or simply compound interest formula.