The value of a certain stock increased by 5% in the first and the second week and dropped by 10% during week 3. How much was the overall change of that stock as a percentage

To calculate the overall percentage change of the stock, we can treat each percentage change sequentially, compounding them step by step.

Let's define the initial value of the stock as \( P_0 = 100 \) (using 100 for simplicity, as it allows us to easily compute percentages).

1. **First week:**
   The stock increased by 5%.
   \[
   P_1 = P_0 \times (1 + 0.05) = 100 \times 1.05 = 105
   \]

2. **Second week:**
   The stock increased again by 5%.
   \[
   P_2 = P_1 \times (1 + 0.05) = 105 \times 1.05 = 110.25
   \]

3. **Third week:**
   The stock dropped by 10%.
   \[
   P_3 = P_2 \times (1 - 0.10) = 110.25 \times 0.90 = 99.225
   \]

Finally, the overall percentage change from the initial value is calculated as:
\[
\text{Overall change} = \left( \frac{P_3 - P_0}{P_0} \right) \times 100 = \left( \frac{99.225 - 100}{100} \right) \times 100 = -0.775\%
\]

So, the overall percentage change is approximately \(-0.775\%\), indicating a slight decrease.

Would you like more details or have any questions?

Here are some related questions:
1. What is the importance of compounding in percentage changes?
2. How would the result differ if the stock had a different sequence of percentage changes?
3. What happens if there is an increase or decrease larger than 100%?
4. How do repeated percentage increases or decreases affect a stock over a long period?
5. Can percentage changes be directly added or do they require compounding?

**Tip:** When dealing with percentage changes, always apply them sequentially (not simply adding or subtracting), as each new percentage is applied to the updated value!

The value of a certain stock increased by 5% in the first and the second week and dropped by 10% during week 3. How much was the overall change of that stock as a percentage?

Learn how to calculate the overall percentage change of a stock after two consecutive 5% increases followed by a 10% drop. This problem uses compounding to demonstrate how percentage changes accumulate over time. Suitable for students in Grades 8-10.

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