# Percent

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Definition.

**Percentage**is one-hundredth part of the number. It is often denoted using the percent sign, "%".

1% | = | 1 | = | 0.01 |

100 |

## Decimal to Percent. Percent to Decimal

- To convert a decimal to a percentage, it must be multiplied by 100.

*For Example*: 4 = 400%; 0.4 = 40%; 0.04 = 4%; 0.004 = 0.4%.

- To convert a percentage to a decimal, it must be divided by 100.

*For Example*: 500% = 5; 50% = 0.5; 5% = 0.05; 0.5% = 0.005.

Definition.

**Compound interest**is the effect often encountered in economics and finance, when the interest income at the end of each period are added to the principal amount and the obtained value in the future becomes a starting point for the calculation of new interest.

## The most common types of problems with percent

- Find P percent of A
- B is P percent of what?
- B is what percentage of A?
- Find the number which is greater (less) than a given number by P percent
- Find the number A if known number B which greater (less) than A by P percent.
- Find the compound interest.

## The method of solving problems with percentage

All ratios and formulas for solving problems with percent, are derived from the proportion.

Data of the tasks with percents can be written as the following relations:

All | - | 100% |

Part | - | Part in % |

which can be written as a proportion

All | = | 100% |

Part | Part in % |

Using this proportion, you can get a formulas for the solution of basic types problems with percent.

## The formulas for the solution of problems with percent

*Formula for finding P percent of number A.*

If given the number A and need to calculate the number B, which is P percent of A, thenB = A · P 100% *Formula for calculating number A when P percent of it is B*A = B · 100% P *B is what percentage of A.*

If we have two numbers A and B and we need to find what percentage of A is B, thenP = B · 100% A *Formula for calculating number B which is greater than A by P percent.*

If we have number A and need to find number B, which greater than A by P percent, thenB = A(1 + P ) 100% *Formula for calculating number B which is less than A by P percent.*

If we have number A and need to find number B, which less than A by P percent, thenB = A(1 - P ) 100% *The formula for calculating the number A If you know the number B, which is greater than A by P percent.*

If the number B is greater than A by P percent, thenA = B · 100% 100% + P *The formula for calculating the number A If you know the number B, which is less than A by P percent.*

If the number B is less than A by P percent, thenA = B · 100% 100% - P *A formula for calculating annual compound interest*

where P - future value;P = A(1 + I ) ^{n}100%

A - is the original principal;

I - nominal annual interest rate in percentage terms;

n - number of compounding periods.

## Examples of solving problems with percent

Example 1.

Find number B which is equal to 5% of 20.**Solution.**

B = | 20 · 5% | = 1 |

100% |

**Answer:**B = 1.

Example 2.

35 is what percent of 20.**Solution.**

35 | · 100% = 175% |

20 |

**Answer:**175%.

Example 3.

Find the number which is less than 20 by 15%.**Solution.**

20(1 - | 15% | ) = 20 · 0.85 = 17 |

100% |

**Answer:**17.

Example 4.

Find profits from the $ 30,000 deposit for 3 years at 10% per annum, if at the end of each year interest is added to your deposit.**Solution.**We use the formula for the calculation of compound interest:

B = 30,000(1 + | 10% | )^{3} = 30,000 · 1.1^{3} = 39,930 |

100% |

**Answer:**profit is $ 9,930.

Percent
Percent Definition. Main information
Decimal to Percent. Percent to Decimal
The method of solving problems with percentage

The most common types of problems with percent:
Find P percent of A
B is P percent of what?
B is what percent of A?
Find the number which is greater (less) than a given number by P percent.
Find the number A if known number B which greater (less) than A by P percent.

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