https://file.aiquickdraw.com/mathbot/file/17282220692994ql6uo8o.jpg

This problem can be solved using the formula for compound interest, which is:

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

Where:

- $ A $ is the final amount (\$679,800).
- $ P $ is the initial principal (\$0.10).
- $ r $ is the annual growth rate (which we want to find).
- $ n $ is the number of years between 1936 and 2020, which is $2020 - 1936 = 84$ years.

Rearrange the formula to solve for the rate $ r $:

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

\[
(1 + r)^n = \frac{A}{P}
\]

\[
1 + r = \left( \frac{A}{P} \right)^{1/n}
\]

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

Now substitute the values:

\[
r = \left( \frac{679,800}{0.10} \right)^{1/84} - 1
\]

\[
r = \left( 6,798,000 \right)^{1/84} - 1
\]

Let's calculate this step-by-step.

### Step 1: Calculate $\left( \frac{679,800}{0.10} \right)^{1/84}$

\[
6,798,000^{1/84} \approx 1.2399
\]

### Step 2: Subtract 1

\[
r \approx 1.2399 - 1 = 0.2399
\]

### Step 3: Convert to Percentage

\[
r \times 100 = 23.99\%
\]

### Final Answer

The annual increase in the value of the comic book is approximately **23.99%**.

Would you like me to go over any part of the calculations in more detail?

Here are some related questions to expand your understanding:

1. How would the result change if the final auction price was different?
2. What if the comic book was sold in 2010 instead of 2020—how would that affect the growth rate?
3. How can you interpret the meaning of the annual increase percentage in practical terms?
4. How does this formula relate to other scenarios involving compound interest?
5. What happens if the value decreases instead of increases—how would the formula change?

**Tip:** Always ensure you convert rates into percentages by multiplying by 100, and use the correct number of decimal places as required.

Assume that in 2020, the first edition of a comic book was sold at auction for $679,800. The comic book was originally sold in 1936 for $0.10. What was the annual increase in the value of the comic book?

Learn how to calculate the annual increase in the value of a comic book from 1936 to 2020, given an initial value of $0.10 and a final auction price of $679,800. This problem covers concepts of compound interest and exponential growth, suitable for high school students in Grades 10-12.

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