Consider the following observations for a time series:

Year 1	Year 2	Year 3	Year 4
99	119	159	169
Calculate the compound growth rate.

The compound growth rate (CGR) over a period of time can be calculated using the formula:

\[
\text{CGR} = \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{n}} - 1
\]

Where:
- **Final Value** is the value at the end of the period (Year 4),
- **Initial Value** is the value at the start of the period (Year 1),
- **n** is the number of periods (Years in this case).

From the data given:
- Initial Value (Year 1) = 99
- Final Value (Year 4) = 169
- Number of periods (n) = 3 (since the time series spans from Year 1 to Year 4, the number of years is 4, but the number of periods between them is 3).

Now, let's calculate the CGR:

\[
\text{CGR} = \left( \frac{169}{99} \right)^{\frac{1}{3}} - 1
\]

I'll calculate that now.The compound growth rate (CGR) is approximately **19.51%** per year over the given period.

Do you want more details or have any questions? 

Here are five related questions:
1. How would the compound growth rate change if Year 4 had a higher value?
2. Can the CGR be negative, and in what scenarios would that occur?
3. How is CGR different from average growth rate over the same period?
4. What is the formula for calculating compound growth over non-uniform periods?
5. How does CGR compare to other growth measures in finance or economics?

**Tip**: The compound growth rate assumes growth builds upon previous values, making it useful for understanding exponential growth trends.

Consider the following observations for a time series:

Year 1 Year 2 Year 3 Year 4
99 119 159 169
Calculate the compound growth rate.

Learn how to calculate the compound growth rate for a time series with values: 99, 119, 159, and 169 over four years. This guide includes the key formula for CGR and explanations on exponential growth. Ideal for high school students in Grades 10-12.

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