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Let's solve the problem step by step.

1. **Account I (Simple Interest):**  
   The formula for simple interest is:  
   \[
   A = P(1 + rt)
   \]
   Where:
   - $ A $ is the final amount.
   - $ P = 2300 $ is the initial deposit.
   - $ r = 0.025 $ (2.5% interest rate).
   - $ t = 5 $ years.

   So, for Account I:
   \[
   A = 2300(1 + 0.025 \times 5)
   = 2300(1 + 0.125)
   = 2300 \times 1.125
   = 2587.50
   \]

2. **Account II (Compound Interest):**  
   The formula for compound interest is:  
   \[
   A = P \left(1 + \frac{r}{n}\right)^{nt}
   \]
   Where:
   - $ P = 2300 $,
   - $ r = 0.025 $,
   - $ n = 1 $ (compounded annually),
   - $ t = 5 $.

   So, for Account II:
   \[
   A = 2300 \left(1 + \frac{0.025}{1}\right)^{1 \times 5}
   = 2300(1.025)^5
   \]
   Let's calculate $ 1.025^5 $ first, then multiply by 2300. I'll compute this now.For **Account II** (compound interest), the final balance after 5 years is approximately **$2602.24**.

3. **Difference Between the Two Accounts:**  
   Now, we find the difference between the balances of the two accounts:
   \[
   \text{Difference} = 2602.24 - 2587.50 = 14.74
   \]

So, the closest answer to the difference between the two accounts after 5 years is **C) $14.74**.

Would you like further clarification on any part of this solution? Here are 5 related questions:

1. How does simple interest differ from compound interest in terms of growth rate?
2. What is the effect of increasing the interest rate on compound interest?
3. How would the result change if the interest in Account II were compounded monthly instead of annually?
4. Can you explain why compound interest yields more money than simple interest over time?
5. How does the length of time (years) affect the difference between simple and compound interest?

**Tip:** When dealing with investments, compound interest tends to grow faster than simple interest, especially over longer periods.

A deposit of $2300 is made into each of two bank accounts. No additional deposits or withdrawals will be made for 5 years. Account I earns 2.5% annual simple interest. Account II earns 2.5% interest compounded annually. Which amount is closest to the difference between the balances of the two accounts at the end of 5 years?

Calculate the difference in balances between two bank accounts after 5 years with a $2300 deposit each. Account I earns 2.5% simple interest, while Account II earns 2.5% compounded annually. The final difference is approximately $14.74. Ideal for high school students learning about simple and compound interest.

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