To calculate how much money you would have after 40 days if your $10 increases by 5% every day, we'll use the same formula for compound interest:

\[
A = P \times \left(1 + \frac{r}{100}\right)^n
\]

Where:
- $ P = 10 $ dollars (initial amount),
- $ r = 5\% $ (daily increase rate),
- $ n = 40 $ days.

Substituting these values:

\[
A = 10 \times \left(1.05\right)^{40}
\]

Let's calculate this.

\[
A = 10 \times 7.04 = 70.4
\]

After 40 days, you would have approximately **$70.40**.

Would you like a detailed explanation, or do you have any questions?

Here are some related questions:

1. What happens to the total if the daily increase is less than 5%?
2. How does increasing the initial amount affect the final value?
3. What if you compounded the interest twice a day instead of once?
4. How would the calculation differ if it was compounded weekly?
5. What are some strategies for maximizing compound interest in savings?
6. Can you derive the formula for compound interest from basic principles?
7. What would be the result if the money grew at a continuous rate?
8. How does this concept apply to loans and mortgages?

**Tip:** Increasing the frequency of compounding periods (like daily vs. monthly) can lead to a higher final amount.

Learn how to calculate compound interest when $10 increases by 5% daily over 40 days. This problem uses the compound interest formula A = P * (1 + r/100)^n, demonstrating exponential growth. Suitable for high school students.

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