The doubling time of an investment is the amount of time it takes to double in value. If an investment with 3.5​% annual compound interest is worth ​$2000​, find its doubling time.
The doubling time is 
  
enter your response here years.

To find the doubling time of an investment with an annual compound interest rate, we can use the Rule of 70, which gives a quick approximation, or we can use the formula for compound interest. Here's how we can proceed:

### Using the Doubling Time Formula
The formula for the doubling time $ T $ in years for an investment with a compound interest rate $ r $ is:
\[
T = \frac{\ln(2)}{\ln(1 + r)}
\]

Given:
- Annual interest rate $ r = 3.5\% = 0.035 $

Now plug this into the formula:
\[
T = \frac{\ln(2)}{\ln(1 + 0.035)}
\]

Let's calculate this.The doubling time for an investment with a 3.5% annual compound interest rate is approximately **20.15 years**.

Would you like more details on the calculation or have any questions? 

Here are some related questions that might interest you:
1. How does the Rule of 70 provide an approximation for doubling time?
2. What happens to the doubling time if the interest rate changes?
3. How does compound interest differ from simple interest in terms of growth?
4. Can the doubling time formula be used for different compounding periods (e.g., monthly or daily)?
5. How does the initial amount of investment affect the doubling time?

**Tip:** Doubling time gives you a quick way to estimate how long it takes for an investment to grow, which is crucial for understanding the power of compound interest.

The doubling time of an investment is the amount of time it takes to double in value. If an investment with 3.5% annual compound interest is worth $2000, find its doubling time. The doubling time is ___ years.

Find the doubling time for an investment with a 3.5% annual compound interest rate. This solution includes the use of the doubling time formula and key concepts like logarithms and exponential growth. Suitable for students in Grades 10-12.

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