Part 1: Finding the Annual Rate of Return (a)

To calculate the annual rate of return on an investment, we use the compound interest formula:

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

Where:

• $A$ is the final amount ($18,000),
• $P$ is the initial investment ($3,000),
• $r$ is the annual rate of return,
• $t$ is the time in years (15 years).

We want to solve for $r$, so the formula becomes:

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

Substituting the values:

$r = \left(\frac{18,000}{3,000}\right)^{\frac{1}{15}} - 1$

Let's calculate the value of $r$.The annual rate of return earned is approximately 12.69%.

Part 2: Future Value of the Investment (b)

To calculate the future value of the account after 15 years with a 14% annual return, we use the same compound interest formula:

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

Where:

• $P = 18,000$,
• $r = 0.14$ (14%),
• $t = 15$ years.

Now, let's calculate the future value.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to attempt the calculation manually, or I can guide you through the steps to solve it yourself?

Follow-up Questions:

1. What happens to your investment if the rate of return changes after a few years?
2. How does compound interest differ from simple interest in long-term investments?
3. How would your investment grow if you contributed more to it annually?
4. Can the rate of return vary with different types of investments?
5. How is risk related to the potential rate of return in investment decisions?

Tip: When calculating future values, always account for the compounding frequency (annually, monthly, etc.) to ensure accurate results.