There are 3 categories of percentage increase problems.
Sales tax is an easy way to illustrate this.
A)
TOTAL = Net Price + (Net Price • Tax Rate)
If we buy an item that will be taxed,
the total amount equals the untaxed price (or net price) plus the net price times the tax rate. Example What is the total cost if a $24 item is taxed at 5%?
5% means 5 for every hundred so 5% = 5 ÷ 100 = .05
TOTAL = $24.00 + (24.00 • .05)
TOTAL = $24.00 + 1.20
TOTAL = $25.20
Basically, this was the same as asking what is 24 increased by 5% ?
B) Tax Rate = (Total ÷ Net Price) -1 Example If a $24 item costs $25.20 when taxed, what is the tax rate?
Tax Rate = (25.20 ÷ 24.00) -1
Tax Rate = 1.05 -1
Tax Rate = .05
If you need to express this as percentage, multiply by 100 to get 5%.
Basically this was the same as asking, if $24 is increased to $25.20 what is the
percentage increase ?
C) Net Price = Total ÷ (Tax Rate +1)
Example If an item costs $25.20 including a 5% tax, what is the
net price ?
Net Price = $25.20 ÷ (1.05)
Net Price = $24.00
Basically this was the same as asking, $25.20 is a 5% increase of what
number ?
Percentage Increase Calculator
In order to use this calculator, first click the category (A, B or C),
then enter the numbers in the first and third boxes, then click CALCULATE.
Do not enter dollar signs, percent signs or commas.
Use the above 3 examples for practice.
Percentage Decrease Tutorial
There are 3 categories of percentage decrease problems.
Income tax is an easy way to illustrate this.
A) NET PAY = Gross Pay - (Gross Pay • Tax Rate)
You earn $325 and it will be taxed 20%. What is your net pay ?
NET PAY = $325.00 - (325.00 • .2)
NET PAY = $325.00 - $65.00
NET PAY = $260.00
Basically, this was the same as asking what is $325 decreased by 20% ?
B) TAX RATE = 1 - ( Net Pay ÷ Gross Pay) Example Your gross pay is $325.00 and your net pay is $260.00.
What is the tax rate?
Tax Rate = 1 - ($260.00 ÷ $325.00)
Tax Rate = 1 - .8
Tax Rate = .2
If you need to express this as a percentage, multiply by 100 to get 20%.
Basically this was the same as asking, if $325 is decreased to $260
what is the percentage decrease ?
C) GROSS PAY = Net Pay ÷ (1 - Rate) Example If your net pay is $260 and the tax rate is 20%, what
is your gross pay ?
Gross Pay = $260.00 ÷ (1 - .2)
Gross Pay = $260.00 ÷ .8
Gross Pay = $325.00
Basically this was the same as asking, $260 is a 20% decrease of what
number ?
Percentage Decrease Calculator
In order to use this calculator, first click the category (A, B or C),
then enter the numbers in the first and third boxes, then click CALCULATE.
Do not enter dollar signs, percent signs or commas.