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## User Guide

This tool will help you calculate percentage values using the various methods of changing a base value into a new one by a set percentage.

### Answer Modes

#### Basic Percent Value

Use this method to calculate either of the parameters involved in determining the proportion of a value equivalent to a defined percentage. e.g. 15% of 270 is 40.5. You can choose to calculate the percentage value, original value or the percent number.

#### Percentage Increase

This method is used to calculate either of the parameters involved in adding the proportion of a value to the original value. e.g. 15% increase on 270 is 310.5. This method is often used to calculate how much tax or interest should be added to a value, or how much to markup a price. You can choose to determine the final value, proportional amount of increase, starting value, or percent increase.

#### Percentage Decrease

This method is used to calculate either of the parameters involved in subtracting the proportion of a value from the original value. e.g. 15% decrease on 270 is 229.5. This method is often used to calculate how much the price of an item is discounted, or in reverse it can be used to set a selling price based on a required % profit margin. You can choose to determine the final value, proportional amount of decrease, starting value, or the percent decrease.

#### Compounding

This calculation type is used to calculate any of the parameters that are involved in increasing an initial value multiple times by a fixed percentage rate. This compounding technique is often used in calculating how much bank loan interest will be charged, or bank savings interest will be paid over a long period of time. e.g. a bank loan at 15% per annum, for a loan of £270, paid back after 3 years, would cost £140.64. You can choose to select the final total, the amount of compounded increase, initial value, percentage rate, equivalent compounded percent number, or the number of times it will take to compound.

### Formulas

The formulas used by this percentage calculator to determine each individual parameter are as follows:

#### Basic

D = S · pc / 100

S = 100 · D / pc

pc = 100 · D / S

#### % Increase

E = S · (100 + pc) / 100

D = S · pc / 100

S = 100 · E / (100 + pc)

pc = (100 · E / S) – 100

#### % Decrease

E = S · (100 – pc) / 100

D = S · pc / 100

S = 100 · E / (100 – pc)

pc = 100 – (100 · E / S)

#### Compounding

E = S · ((100 + pc)/100)ⁿ

D = S · ((100 + pc)/100)ⁿ – S

S = E / ((100 + pc)/100)ⁿ

pc = (E / S)^{1/n} · 100) – 100

pcn = (((100 + pc) / 100)ⁿ · 100) – 100

n = ln(E / S) / ln((100 + pc) / 100)

#### Symbols

- S = Start value
- D = Difference between start and end value
- E = End value
- pc = percent value
- pcn = compounded percent value
- n = number of times to compound percentage increase

### Parameters

#### Start Value

This is the original value you start with before applying any percentage calculation

#### Percentage (%)

This is the proportion of something as a percentage, and 1 percent is equivalent to a fraction of 1/100th or 0.01.

In the context of this calculator, the percentage is the proportion to find of a value, to apply an increase or a decrease in a value, the rate to compound, or the effective percentage increase due to the compounding of a percentage rate, n times.

#### Number Of Times (n)

This is the number of times to compound a percentage rate, or how many times to increase a value by a set percentage rate. e.g. 3% compounded 3 times means 1.03 x 1.03 x 1.03 = 1.0927.

#### % Value

This is the difference between the start and end value, which also represents the proportion of the start value that corresponds to the required percentage.

#### End Value

This is the final value you are left with after applying the percentage calculation.