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## Introduction:

Hello Challenger, welcome to our article on how to find percentage. In this step-by-step guide, we will show you how to calculate percentages in different scenarios. Whether you are a student, a business owner, or just looking to brush up on your math skills, this article will provide you with everything you need to know to find percentage quickly and easily. Let’s get started!

### What is Percentage?

Percentage is a way of expressing a number as a fraction of 100. It is used in many different contexts, from calculating test scores to determining discounts on products. The symbol used for percentage is “%”. For example, if you score 80 out of 100 on a test, your percentage score is 80%.

### When to Use Percentage?

Percentage is used to compare different quantities or to express part of a whole. For example, it can be used to calculate tax on a purchase, to determine the discount on a product, or to compare the number of male and female students in a class. Understanding how to use percentages can be helpful in everyday life and in many different professions.

### Why is Finding Percentage Important?

Percentage helps us to understand the relationship between two numbers and is commonly used in everyday life. For example, businesses use percentage to calculate discounts, interest rates, and profit margins. Additionally, students use percentage to calculate their grades, and homeowners use percentage to calculate their mortgage payments.

### Types of Percentage Problems

There are three main types of percentage problems: finding the percentage of a number, working out the percentage increase or decrease, and calculating compound interest. In the following sections, we will discuss each of these in more detail.

## How to Find Percentage?

### 1. Finding the Percentage of a Number

The first type of percentage problem is finding the percentage of a number. This is often used to calculate discounts or to determine how much tax is owed on a purchase.

#### Formula:

To find the percentage of a number, you need to multiply the number by the percentage as a decimal. The formula for this is:

Number | Percentage | Result |
---|---|---|

50 | 30% | 15 |

100 | 25% | 25 |

75 | 50% | 37.5 |

#### Example:

If you want to know what 30% of 50 is, you would use the formula: 50 x 0.30 = 15. Therefore, 30% of 50 is 15.

#### Steps:

The steps to find the percentage of a number are:

- Convert the percentage to a decimal by dividing by 100.
- Multiply the decimal by the number you want to find the percentage of.
- The result is the answer in percentage form.

#### Application:

Suppose you want to buy a shirt that costs $40, but it is on sale for 20% off. Using the formula, you would calculate the discount as follows: 40 x 0.20 = 8. Therefore, the amount of the discount is $8, and the sale price is $32 ($40 – $8).

### 2. Percentage Increase or Decrease

The second type of percentage problem is calculating percentage increase or decrease. This can be used to determine salary increases or decreases, or to calculate how much a stock has gone up or down.

#### Formula:

To calculate the percentage increase or decrease, you need to use the following formula:

Old Value | New Value | Percentage Change |
---|---|---|

100 | 120 | 20% |

75 | 60 | -20% |

50 | 75 | 50% |

#### Example:

If you want to know the percentage increase or decrease if the value of a product goes from $100 to $120, you would use the formula: (20/100) x 100 = 20%. Therefore, the value of the product increased by 20%.

#### Steps:

The steps to calculate percentage increase or decrease are:

- Calculate the difference between the old value and the new value.
- Divide the difference by the old value.
- Multiply the result by 100 to get the answer in percentage form.

#### Application:

Suppose you want to know what percentage your salary has increased from $80,000 to $90,000. Using the formula, you would calculate the percentage increase as follows: ((90,000 – 80,000) / 80,000) x 100 = 12.5%. Therefore, your salary increased by 12.5%.

### 3. Compound Interest

The third type of percentage problem is calculating compound interest. This is often used to calculate interest on loans or investments.

#### Formula:

The formula for compound interest is:

A = P (1 + r/n) ^ nt

Where:

- A is the total amount after n years including interest
- P is the principal amount (the initial amount you borrowed or deposited)
- r is the annual interest rate (as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years

#### Example:

If you invested $10,000 at an annual interest rate of 5%, compounded annually for 10 years, you would have:

A = 10,000 (1 + 0.05/1) ^ (1 x 10)

A = 16,386.17

Therefore, you would have $16,386.17 after 10 years, with a total interest amount of $6,386.17.

#### Steps:

The steps to calculate compound interest are:

- Determine the principal amount, interest rate, number of times per year the interest is compounded, and the number of years.
- Calculate the amount of interest earned for each compounding period.
- Add the interest earned to the principal amount to get the new principal amount for the next compounding period.
- Repeat the calculations for the remaining compounding periods.

#### Application:

Suppose you have a $5,000 loan with an annual interest rate of 8%, compounded monthly, and you make monthly payments of $150. Using the formula, you would calculate the remaining balance on the loan after 5 years as follows:

- P = 5,000
- r = 0.08/12 = 0.0067 (monthly interest rate)
- n = 12 (compounding periods per year)
- t = 5 x 12 = 60

A = 150 [(1 + 0.0067) ^ 60 – 1] / 0.0067 + 5,000 [(1 + 0.0067) ^ 60] = $4,601.61

Therefore, after 5 years, the remaining balance on the loan would be $4,601.61.

## FAQs About Finding Percentage:

### 1. How do I convert percentage to a decimal?

To convert a percentage to a decimal, divide it by 100. For example, to convert 75% to a decimal, you would divide 75 by 100, which equals 0.75.

### 2. Can I use a calculator to find percentage?

Yes, you can use a calculator to find percentage. Most calculators have a percentage button that can be used to perform calculations quickly and easily.

### 3. What is the percentage increase and decrease formula?

The formula for percentage increase or decrease is: ((new value – old value) / old value) x 100. For example, if the old value is 100 and the new value is 120, the percentage increase is: ((120 – 100) / 100) x 100 = 20%.

### 4. How do you find the percentage of a discount?

To find the percentage of a discount, you need to subtract the sale price from the original price and then divide that amount by the original price. You then multiply the result by 100 to get the percentage of the discount. For example, if a product costs $50 and is on sale for $40, you would calculate the discount as follows: ((50 – 40) / 50) x 100 = 20%.

### 5. Can percentage be more than 100%?

No, percentage cannot be more than 100%. This is because percentage is a way of expressing a number as a fraction of 100.

### 6. How do you calculate annual percentage rate?

The formula to calculate annual percentage rate is:

APR = (2 x Monthly Interest Rate x Number of Months) / (Number of Months + 1)

### 7. How do you calculate percentage gain?

The formula to calculate percentage gain is: (Change in Value / Original Value) x 100. For example, if a stock increases from $50 to $75, the percentage gain is: ((75 – 50) / 50) x 100 = 50%.

## Conclusion:

In conclusion, understanding how to find percentage can be useful in many different areas of life, from calculating grades to making financial decisions. Whether you are dealing with percentage increase or decrease or calculating compound interest, the formulas and steps outlined in this article will help you solve any percentage problem quickly and easily. We hope this guide has been helpful to you and encourages you to apply these concepts in your daily life.

### Take Action:

Now that you have learned how to find percentage, it’s time to put this knowledge into practice. Try solving some percentage problems on your own or use our table to help you practice. The more you practice, the better you will become at finding percentages.

## Disclaimer:

This article is for educational purposes only and should not be used as a substitute for professional advice. The information presented here is accurate to the best of our knowledge as of the time of writing. However, we make no guarantees as to the accuracy or completeness of the information presented herein. We are not responsible for any errors or omissions, or for any loss or damage of any kind arising from the use of this article or its contents.