Question

Gdp is $20 trillion, how many years will it take for gdp to increase to $160 trillion if annual growth is 10 percent?

Answer 1

To calculate how long it will take for the GDP to increase to $160 trillion with an annual growth rate of 10%, we can use the compound interest formula. Using this formula, it will take approximately 26.03 years for the GDP to reach $160 trillion.

Step-by-step explanation:

To calculate the number of years it would take for GDP to grow from $20 trillion to $160 trillion with an annual growth rate of 10 percent, you can use the formula for compound interest:

`\[ \text{Future Value} = \text{Present Value} * (1 + \text{Growth Rate})^{\text{Number of Years}} \]`

Given:

- Present Value (GDP) = $20 trillion

- Future Value (desired GDP) = $160 trillion

- Annual Growth Rate = 10% or 0.1

Let's plug these values into the formula and solve for the number of years:

`\[ \text{Future Value} = \text{Present Value} * (1 + \text{Growth Rate})^{\text{Number of Years}} \]`

`\[ 160 = 20 * (1 + 0.1)^{\text{Number of Years}} \]`

Divide both sides by 20:

`\[ 8 = (1.1)^{\text{Number of Years}} \]`

Taking the logarithm of both sides to solve for the number of years:

`\[ \log{8} = \text{Number of Years} * \log{1.1} \]`

`\[ \text{Number of Years} = \frac{\log{8}}{\log{1.1}} \]`

Using a calculator:

`\[ \text{Number of Years} \approx (0.9031)/(0.0414) \approx 21.77 \]`

Therefore, it would take approximately 21.77 years for the GDP to increase from $20 trillion to $160 trillion with an annual growth rate of 10 percent.