In 1950 GDP in the United Kingdom (measured in year 2005 pounds) was ₤317 billion. In 2000, it was ₤1,108 billion. Calculate the growth rate of real GDP in the United Kingdom over this period. Now suppose that the United Kingdom grows at the same rate for the 50 years following 2000. What will the UK real GDP be in the year 2050?

To calculate the growth rate of real GDP over a given period, we use the **compound annual growth rate (CAGR)** formula:

\[
\text{CAGR} = \left( \frac{V_f}{V_i} \right)^{\frac{1}{t}} - 1
\]

Where:
- \(V_f\) is the final value (GDP in 2000)
- \(V_i\) is the initial value (GDP in 1950)
- \(t\) is the time period in years (from 1950 to 2000, so \(t = 50\))

### Step 1: Calculate the growth rate from 1950 to 2000

Given:
- \(V_i = 317 \, \text{billion pounds}\)
- \(V_f = 1108 \, \text{billion pounds}\)
- \(t = 50 \, \text{years}\)

We can now substitute these values into the CAGR formula:

\[
\text{CAGR} = \left( \frac{1108}{317} \right)^{\frac{1}{50}} - 1
\]

Let me compute this.The compound annual growth rate (CAGR) of real GDP in the United Kingdom from 1950 to 2000 is approximately **2.53%**.

### Step 2: Projecting the GDP in 2050

Now, we assume that the GDP continues to grow at the same rate for the next 50 years. To find the projected GDP in 2050, we use the formula for future value in compound growth:

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

Where:
- \(V_f = 1108\) billion pounds (GDP in 2000)
- \(\text{CAGR} = 0.025344\) (annual growth rate)
- \(t = 50\) years

Let me calculate the projected GDP for 2050.The projected real GDP of the United Kingdom in the year 2050, assuming it grows at the same rate of approximately 2.53% per year, is approximately **₤3,873 billion** (in year 2005 pounds).

Would you like more details on any of these calculations or have further questions?

Here are five related questions for deeper understanding:
1. How is the compound annual growth rate (CAGR) derived?
2. What factors can influence real GDP growth rates over long periods?
3. How does inflation differ from real GDP growth?
4. What would happen if the growth rate changes to a higher or lower value in the future?
5. How do historical growth rates of different countries compare?

**Tip**: Compound interest is not only useful for economic data but also for personal finance, such as calculating investment growth.

Learn how to calculate the Compound Annual Growth Rate (CAGR) of real GDP in the United Kingdom from 1950 to 2000, with a detailed step-by-step solution. Also, project the real GDP for 2050 assuming the same growth rate. The initial GDP in 1950 was ₤317 billion, and in 2000 it was ₤1,108 billion. This problem is ideal for students in Grades 11-12 studying advanced economics or mathematics.

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