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Algebra Financial mathematics

Percent change in context

20 practice questions 2 video lessons Theory + worked examples
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Theory

Percent change compares a new value with the original:
\[\%\text{ change}=\dfrac{\text{new}-\text{old}}{\text{old}}\times100.\]
  • Positive: an increase (markup).
  • Negative: a decrease (discount).
Increase by \(r\): multiply by \(1+r\). Decrease: multiply by \(1-r\).
Percent change Percent change Percent change % change = (new - old) / old × 100 positive: increase negative: decrease
The percent change formula.
Example Example Example price 50 → 65 (65 - 50) / 50 = 0.30 = 30% increase
A worked example.

Percent change:

\[\dfrac{\text{new}-\text{old}}{\text{old}}\times100\]
new minus old over old, times 100
Always divide by the original (old) value.

How to find percent change

  1. Subtract old from new.
  2. Divide by the old value.
  3. Multiply by \(100\).
  4. Positive means increase, negative means decrease.
Example 1 — Percent increase
A price rises from \(\$50\) to \(\$65\). Find the percent change.
Solution

Use \(\dfrac{\text{new}-\text{old}}{\text{old}}\).

\(\dfrac{65-50}{50}\)\(=\)\(0.30=30\%\)
a 30 percent increase
Example 2 — Percent decrease
A value falls from \(\$80\) to \(\$60\). Find the percent change.
Solution

A drop is negative.

\(\dfrac{60-80}{80}\)\(=\)\(-0.25=-25\%\)
a 25 percent decrease
Example 3 — Apply a percent
Increase \(\$40\) by \(15\%\).
Solution

Multiply by \(1.15\).

\(40(1.15)\)\(=\)\(\$46\)
46 dollars
Example 4 — Discount
A \(\$60\) item is \(20\%\) off. Find the sale price.
Solution

Multiply by \(0.80\).

\(60(0.80)\)\(=\)\(\$48\)
48 dollars

Common pitfalls

Divide by the original value, not the new one.
A decrease is negative.
Markup: \(\times(1+r)\); discount: \(\times(1-r)\).

Frequently asked questions

How do you find percent change?

\(\dfrac{\text{new}-\text{old}}{\text{old}}\times100\).

What does a negative percent change mean?

A decrease.

How do you increase a value by \(15\%\)?

Multiply by \(1.15\).

How do you apply a \(20\%\) discount?

Multiply by \(0.80\).

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