Percent Change Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

hard
A stock price rises by 20%20\% one year and falls by 20%20\% the next year. If it started at \100$, what is the final price and the overall percent change?

Solution

  1. 1
    After a 20%20\% increase: 100 \times 1.20 = \120$.
  2. 2
    After a 20%20\% decrease from \120:: 120 \times 0.80 = \9696.
  3. 3
    Overall change: 100−96100×100%=4%\frac{100 - 96}{100} \times 100\% = 4\% decrease.

Answer

$96, a 4% overall decrease\$96, \text{ a } 4\% \text{ overall decrease}
Equal percentage increases and decreases do not cancel out. The decrease is applied to a larger base, resulting in a net loss. This is an important concept in financial mathematics.

About Percent Change

Percent change measures how much a quantity has increased or decreased relative to its original value, calculated as new−originaloriginal×100%\frac{\text{new} - \text{original}}{\text{original}} \times 100\%.

Learn more about Percent Change →

More Percent Change Examples

Example 1 easy

A jacket originally costs [formula]60[formula][formula]. What is the percent decrease?

Example 2 medium

A town's population grew from [formula] to [formula]. What is the percent increase?

Example 4 easy

A shirt's price increases from [formula]25[formula][formula]. What is the percent increase?

Example 5 medium

After a [formula] discount, a laptop costs [formula]680$. What was the original price?

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