Percentage Change

Important Words

Discount

An amount the original price is being lowered by.

Mark down

An amount the original price is being lowered by.

Increase

An amount the original price is being raised by.

Important Formulas

The following formulas use these variables:

• C is the amount the price is being changed by;
• P is the original price;
• r is the interest rate (as a percent).
• N is the new price.

To find a price change ("of"):

(1)

\begin{align} C = \frac{P \times r}{100} \end{align}

To find a new price after a price increase ("mark up", "price rise", "premium"):

(2)

\begin{align} N = P + C = P \times \left( 1 + \frac{r}{100} \right) \end{align}

To find a new price after a price decrease ("mark down", "discount", "off"):

(3)

\begin{align} N = P - C = P \times \left( 1 - \frac{r}{100} \right) \end{align}

To find a percentage change:

(4)

\begin{align} r = \frac{C}{P} \times 100 \end{align}

To find an original price after a price change:

(5)

\begin{align} P = N \times \frac{100}{(r - 100)} \end{align}

for a price that was decreased, or

(6)

\begin{align} P = N \times \frac{100}{(r + 100)} \end{align}

for a price that was increased.

References

Jones, et al. Essential Standard General Mathematics, Cambridge University Press, First Edition (2005), pp209-213.