To calculate the total percentage increase over two years, we need to account for the fact that the increases are compounded year-over-year. Here's how we can do it:

Step-by-Step Calculation:

1. Let the initial profit be $P$.
2. In the first year, the profit increases by 15%, so the profit after the first year is: $P \times (1 + 0.15) = P \times 1.15$
3. In the second year, the profit increases by 20% on the new amount, so the profit after the second year is: $P \times 1.15 \times (1 + 0.20) = P \times 1.15 \times 1.20 = P \times 1.38$
4. The total profit after two years is $P \times 1.38$, meaning the profit has increased by 38% over the two years.

Thus, the total percentage increase over the two years is 38%.

Would you like any further explanation or details?

Here are 5 related questions to consider:

1. How would the total increase change if the percentages were reversed (20% in the first year and 15% in the second)?
2. What would the percentage increase be if the company had a 10% decrease in the third year?
3. How do you calculate the percentage change if there are different changes across several years?
4. What if the company saw a 0% increase in the second year? How would the total increase be affected?
5. How can you express the relationship between compounded growth rates mathematically?

Tip: For multiple year percentage increases, always compound the growth rates instead of simply adding them together.