In 1899, the first Green Jacket Golf Championship was held. The winner’s prize money was $235. In 2020, the winner’s check was $2,670,000.

What was the annual percentage increase in the winner’s check over this period?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

If the winner’s prize increases at the same rate, what will it be in 2055?

Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 1,234,567.89.

To determine the annual percentage increase in the winner’s check over the period from 1899 to 2020, we will use the **compound annual growth rate (CAGR)** formula. The formula is:

\[
\text{CAGR} = \left( \frac{ \text{Ending Value} }{ \text{Starting Value} } \right)^{ \frac{1}{n} } - 1
\]

Where:
- $\text{Ending Value} = 2,670,000$ (the prize in 2020)
- $\text{Starting Value} = 235$ (the prize in 1899)
- $n = 2020 - 1899 = 121$ years

### Step 1: Calculate the annual percentage increase (CAGR)
Let's first calculate the CAGR.

\[
\text{CAGR} = \left( \frac{2,670,000}{235} \right)^{\frac{1}{121}} - 1
\]

### Step 2: Use this rate to calculate the prize in 2055
Once we have the growth rate, we can calculate the prize in 2055 using the formula for compound growth:

\[
\text{Future Value} = \text{Starting Value} \times (1 + r)^{t}
\]

Where:
- $r$ is the annual percentage increase (from the first part)
- $t = 2055 - 2020 = 35$ years
- $\text{Starting Value} = 2,670,000$

I'll now calculate both the CAGR and the future value for 2055.The annual percentage increase in the winner’s check from 1899 to 2020 is **8.02%**.

If the winner’s prize increases at the same rate, the prize in 2055 will be approximately **$39,771,631.02**.

Would you like more details or have any further questions? Here are some related questions for exploration:

1. How does compound growth differ from simple interest growth?
2. What factors could influence changes in the growth rate of such prizes?
3. Can the CAGR formula be applied to population growth? How?
4. How does inflation impact real prize value over time?
5. What would the prize be in 2100 if the rate continued at 8.02%?

**Tip:** The compound annual growth rate is widely used to measure investment returns and growth over extended periods, smoothing out yearly fluctuations.

In 1899, the first Green Jacket Golf Championship was held. The winner’s prize money was $235. In 2020, the winner’s check was $2,670,000. What was the annual percentage increase in the winner’s check over this period? If the winner’s prize increases at the same rate, what will it be in 2055?

Learn how to calculate the annual percentage increase in the winner’s prize from 1899 to 2020 using the compound annual growth rate (CAGR) formula. Discover what the prize could be in 2055 with this detailed solution, involving exponential growth and key financial mathematics concepts. Ideal for high school students in Grades 10-12.

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