The problem presents two savings accounts:

• Account A: Earns $100 in interest each year (simple interest).
• Account B: Earns 5% of the account balance as interest each year (compound interest).

We are asked to identify the correct statement that describes how the interest and growth relationship works for each account after 4 years.

Let's break down the options:

1. Account A earns simple interest and shows linear growth because the interest earned is the same each year. Account B earns compound interest and shows exponential growth because the interest earned increases each year.

   • This is the correct statement. Account A follows a simple interest pattern, meaning the same amount ($100) is added each year. Account B earns compound interest, where the interest is calculated on the growing balance, so the amount increases each year, leading to exponential growth.

2. Both Account A and Account B earn simple interest and show linear growth because the interest rates do not change.

   • This is incorrect because Account B earns compound interest, not simple interest. Compound interest leads to exponential growth.

3. Both Account A and Account B earn compound interest and show an exponential growth because the interest is calculated annually.

   • This is incorrect. Account A earns simple interest, not compound interest.

4. Account A earns compound interest and shows an exponential growth because the interest increases each year. Account B earns simple interest and shows a linear growth because the interest earned is constant each year.

   • This is incorrect. Account A earns simple interest, not compound interest, and Account B earns compound interest, not simple interest.

The correct choice is the first statement, which correctly describes the growth of each account based on the type of interest applied.

Would you like further details or have additional questions on this topic?

Here are some related questions:

1. What is the formula for calculating simple interest?
2. How do you calculate compound interest over multiple periods?
3. How does the principal affect the growth of both simple and compound interest?
4. What are the differences between linear and exponential growth in finance?
5. How can we visualize the growth of investments with simple and compound interest?

Tip: To see the effects of compound interest, it's helpful to graph both simple and compound interest over time to compare their growth rates visually.