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To solve this problem, we’ll calculate the interest for both accounts separately over a period of 24 months (or 2 years), then find the difference between them.

---

### Given Data:
- **Principal (P):** $1750
- **Time (T):** 24 months = 2 years
- **Interest Rate (R):** 2.75% annually

### Account I - Simple Interest
The formula for simple interest is:
\[
\text{Simple Interest (SI)} = P \times R \times T
\]
where:
- $ P = 1750 $
- $ R = 2.75\% = 0.0275 $
- $ T = 2 $ years

Substituting the values:
\[
\text{SI} = 1750 \times 0.0275 \times 2
\]
\[
\text{SI} = 1750 \times 0.055
\]
\[
\text{SI} = 96.25
\]

So, the interest earned in **Account I** is **$96.25**.

---

### Account II - Compound Interest (Compounded Annually)
The formula for compound interest is:
\[
A = P \left(1 + \frac{R}{n}\right)^{nT}
\]
where:
- $ A $ is the amount after interest.
- $ P = 1750 $
- $ R = 2.75\% = 0.0275 $
- $ n = 1 $ (compounded annually)
- $ T = 2 $ years

Substituting the values:
\[
A = 1750 \left(1 + \frac{0.0275}{1}\right)^{1 \times 2}
\]
\[
A = 1750 \left(1 + 0.0275\right)^2
\]
\[
A = 1750 \times (1.0275)^2
\]
Calculating $ (1.0275)^2 $:
\[
1.0275^2 \approx 1.05675625
\]
\[
A = 1750 \times 1.05675625
\]
\[
A \approx 1849.32
\]

To find the interest earned (CI):
\[
\text{CI} = A - P
\]
\[
\text{CI} = 1849.32 - 1750
\]
\[
\text{CI} \approx 99.32
\]

So, the interest earned in **Account II** is approximately **$99.32**.

---

### Difference in Interest Earned:
\[
\text{Difference} = \text{CI} - \text{SI}
\]
\[
\text{Difference} = 99.32 - 96.25
\]
\[
\text{Difference} \approx 3.07
\]

---

### Answer:
The difference between the interest earned in Account II and Account I at the end of 24 months is approximately **$3.07**.

---

Would you like a more detailed breakdown of each calculation step? 

Here are five related questions you could explore:

1. How would the difference change if the interest rate were increased to 3%?
2. What would be the effect if Account II compounded interest semi-annually?
3. How much interest would Ben earn if he invested $2,000 instead of $1,750?
4. What is the total balance in each account at the end of 24 months?
5. How would the difference in interest change if the time period were extended to 5 years?

**Tip:** For compound interest, the frequency of compounding (annually, semi-annually, quarterly, etc.) significantly affects the total amount earned.

Ben deposits $1,750 into each of two savings accounts. Account I earns 2.75% annual simple interest. Account II earns 2.75% interest compounded annually. Ben does not make any additional deposits or withdrawals. What is the difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 24 months?

Learn how to find the difference in interest earned between simple and compound interest for a $1,750 deposit over 2 years at a 2.75% annual rate. Understand key concepts of simple and compound interest with step-by-step calculations. Ideal for students in Grades 9-10.

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