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Module 5: Percents

Percent Change

A percent change describes a change in an amount based on a percentage added or removed from the original amount. This percentage is calculated based on the initial value, and thus is relative to the initial value. If the initial value is small, the percent change will appear larger, whereas a large initial value results in a smaller percent change. Furthermore, this value will be positive in an amount increase and negative in an amount decrease.

The equation is written below:

% c h a n g e = F V − I V I V × 100 % {"version":"1.1","math":"\%change = \dfrac{FV-IV}{IV} \times 100 \% "}

Where:

  • FV = Final value
  • IV = Initial value

Percent Change Example

Consider this two-part question:

  1. If a person started with $179 000 to invest and gains 26%, how much money do they have now?
  2. How much % would they have to lose to get back to the starting amount?

What we know:

I V = 179000 {"version":"1.1","math":"IV=179000 "}

% c h a n g e = 26 % {"version":"1.1","math":"\%\;change = 26\% "}

What we want to know:

FV{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi></math>"}

Solving:

0.26 = F V − 179000 179000 {"version":"1.1","math":"0.26 = \dfrac{FV-179000}{179000} "}

0.26 × 179000 = F V − 179000 179000 × 179000 {"version":"1.1","math":"0.26 \times 179000 = \dfrac{FV-179000}{179000} \times 179000 "}

0.26 × 179000 = F V − 179000 {"version":"1.1","math":"0.26 \times 179000 = FV-179000 "}

0.26 × 179000 + 179000 = F V {"version":"1.1","math":"0.26 \times 179000 + 179000 = FV "}

F V = 225540 {"version":"1.1","math":"FV = 225540 "}

What we know:

F V = 179000 {"version":"1.1","math":"FV = 179000 "}

I V = 225540 {"version":"1.1","math":"IV = 225540 "}

What we want to know:

% c h a n g e {"version":"1.1","math":"\%\;change "}

Solving:

% C h a n g e = 179000 − 225540 225540 × 100 % {"version":"1.1","math":"\%\; Change = \dfrac{179000-225540}{225540} \times 100\% "}

% C h a n g e = − 20.63 % → 20.63 % loss {"version":"1.1","math":"\%\;Change = -20.63\% \rightarrow 20.63\% \: \mathrm{loss} "}

Notice the absolute value of both percent changes are different despite being changes between 225 540 and 179 000. Remember, this comes down to the initial value of the question: the smaller initial value, the greater the percent change appears.

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