# What percent increase is $4-$5?

##### 2 Answers

Going from $4 to $5 is a 25% increase.

#### Explanation:

A **percent increase** is how much the amount gained is, relative to the amount we start with. It's the ratio of the amount gained to the initial amount.

If, for example, you start a chat group with *increase* (in units of people) is

#N-n#

*(This should seem easy.)*

The *relative increase* is this difference of

#(N-n)/n#

and so it has no units. It's like we're asking, "How many groups of size

Finally, the **percent increase** is just the relative increase, expressed as a percentage (which simply involves multiplying the relative increase by 100%):

#(N-n)/n xx 100%#

Using your question as an example, a dollar value has gone from $4 to $5. By the formula above, the percent increase is

#color(white)=(N-n)/nxx 100%#

#=($5-$4)/($4)xx100%#

#=($1)/($4)xx100%#

#= 0.25 xx 100%" "=" "25%#

So the percentage increase of going from $4 to $5 is 25%, because that $1 gain is 25% of the original $4.

## Bonus:

Using some basic algebra, we can simplify the formula for relative increase to:

#(N-n)/n" "=" "N/n - n/n" "=" "N/n - 1#

In this way, the relative increase is the ratio of the new value to the old one, minus 1. Of course, the *percent increase* is still just this relative increase multiplied by 100%:

#(N/n -1 )xx 100%#

Both formulas give the right answer.

#### Explanation:

If we start with

We can do this a couple of different ways. One way is to take the change and divide it by the original:

Another way we can do this is to set up an equation this way:

And yet another is to not calculate the difference first: