You have an investment account that started with 

​$3 comma 0003,000 

1515 

years ago and which now has grown to 

​$18 comma 00018,000.

**a.** What annual rate of return have you earned​ (you have made no additional contributions to the​ account)?

**b.** If the investment account earns 

14 %14% 

per year from now​ on, what will the​ account's value be 

1515 

years from​ now?

Question content area bottom

Part 1

**a.** What annual rate of return have you earned​ (you have made no additional contributions to the​ account)?

Your annual rate of return is 

enter your response here​%. 

 ​(Round to two decimal​ places.

### Part 1: Calculating the annual rate of return

To find the annual rate of return, we can use the **compound interest formula**:

\[
A = P \times (1 + r)^t
\]

Where:
- $A = 18,000$ (the final amount),
- $P = 3,000$ (the initial amount),
- $r$ is the annual interest rate we are trying to find,
- $t = 15$ years (the time period).

Rearranging the formula to solve for $r$:

\[
r = \left(\frac{A}{P}\right)^{\frac{1}{t}} - 1
\]

We can now substitute the known values and solve for $r$.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you on how to calculate it manually:

1. **Step 1:** Use the compound interest formula:
   \[
   r = \left( \frac{A}{P} \right)^{\frac{1}{t}} - 1
   \]
   where $A = 18,000$, $P = 3,000$, and $t = 15$.

2. **Step 2:** Divide the final amount by the initial amount:
   \[
   \frac{A}{P} = \frac{18,000}{3,000} = 6
   \]

3. **Step 3:** Take the 15th root of 6:
   \[
   6^{\frac{1}{15}} \approx 1.127
   \]

4. **Step 4:** Subtract 1 and multiply by 100 to get

You have an investment account that started with $3,000 15 years ago and which now has grown to $18,000. a. What annual rate of return have you earned (you have made no additional contributions to the account)? b. If the investment account earns 14% per year from now on, what will the account's value be 15 years from now?

Find out how to calculate the annual rate of return for an investment that started with $3,000 and grew to $18,000 over 15 years. Learn how to use the compound interest formula and determine the future value of the investment if it continues to earn 14% annually. Suitable for high school students studying exponential growth and compound interest.

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