To solve the equation $1231 = 390 \times \left(1 + \frac{r}{100}\right)^{18}$, follow these steps:

### Step 1: Isolate the exponential expression
First, divide both sides of the equation by 390 to isolate the exponential term:

\[
\frac{1231}{390} = \left(1 + \frac{r}{100}\right)^{18}
\]

Calculate the division on the left-hand side:

\[
\frac{1231}{390} \approx 3.1577
\]

So the equation becomes:

\[
3.1577 = \left(1 + \frac{r}{100}\right)^{18}
\]

### Step 2: Take the 18th root of both sides
To solve for $\left(1 + \frac{r}{100}\right)$, take the 18th root of both sides:

\[
\left(3.1577\right)^{\frac{1}{18}} = 1 + \frac{r}{100}
\]

### Step 3: Compute the 18th root
Calculate the 18th root of 3.1577:

\[
3.1577^{\frac{1}{18}} \approx 1.0663
\]

This gives us:

\[
1.0663 = 1 + \frac{r}{100}
\]

### Step 4: Solve for $r$
Subtract 1 from both sides to isolate $\frac{r}{100}$:

\[
\frac{r}{100} = 0.0663
\]

Multiply both sides by 100 to find $r$:

\[
r \approx 6.63\%
\]

### Final Answer:
The value of $r$ is approximately **6.63%**.

Would you like more details or have any other questions?

Here are some related questions:
1. How does compound interest work in financial calculations?
2. What is the significance of the number 18 in the equation?
3. How would the solution change if the exponent were different?
4. How do you solve exponential equations using logarithms?
5. What happens if the initial value or final value changes in similar equations?

**Tip:** When solving equations involving exponents, taking the root corresponding to the exponent is often a useful step to isolate the base term.

Learn how to solve the compound interest exponential equation $1231 = $390 * (1+r/100)^18 with a step-by-step solution. This problem involves understanding exponential equations and compound interest calculations. Suitable for high school students and learners interested in financial mathematics.

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