A deposit of $3,800 is made into each of two bank accounts. No additional deposits or withdrawals will be made for 5 years.
 

Account I earns 4.2% annual simple interest.

Account II earns 4.2% interest compounded annually.


Which amount is closest to the difference between the balances of the two accounts at the end of 5 years?

A.$165.91 

B.$6.91

C.$69.91

D.$106.91


Let's calculate the balance of both accounts after 5 years, then find the difference between them.

### **Account I: Simple Interest**
The formula for simple interest is:
\[
A = P(1 + rt)
\]
Where:
- $ P = 3800 $ (initial deposit)
- $ r = 0.042 $ (interest rate)
- $ t = 5 $ (years)

Substituting the values:
\[
A = 3800(1 + 0.042 \times 5) = 3800(1 + 0.21) = 3800 \times 1.21 = 4598
\]

So, the balance in Account I after 5 years is **$4598**.

### **Account II: Compound Interest**
The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $ P = 3800 $ (initial deposit)
- $ r = 0.042 $ (interest rate)
- $ n = 1 $ (compounded annually)
- $ t = 5 $ (years)

Substituting the values:
\[
A = 3800 \left(1 + \frac{0.042}{1}\right)^{1 \times 5} = 3800 \left(1 + 0.042\right)^5 = 3800 \times (1.042)^5
\]
Using the power calculation:
\[
(1.042)^5 \approx 1.229416
\]
So:
\[
A \approx 3800 \times 1.229416 = 4671.78
\]

The balance in Account II after 5 years is approximately **$4671.78**.

### **Difference Between the Two Accounts**
Now, let's find the difference between the balances of the two accounts:
\[
4671.78 - 4598 = 73.78
\]

So, the closest answer to the difference is **$69.91**, which corresponds to option **C**.

---

Would you like more details on any step or have additional questions?

Here are 5 related questions:
1. How does the frequency of compounding affect the final balance?
2. What would the balances be with different interest rates?
3. What is the difference if the interest compounds monthly instead of annually?
4. How can we calculate interest for periods shorter than a year?
5. What if additional deposits were made during the 5 years?

**Tip:** Compounding more frequently results in more interest because the interest earned is added back to the principal more often.

A deposit of $3,800 is made into each of two bank accounts. No additional deposits or withdrawals will be made for 5 years.

Account I earns 4.2% annual simple interest.

Account II earns 4.2% interest compounded annually.

Which amount is closest to the difference between the balances of the two accounts at the end of 5 years?

A.$165.91
B.$6.91
C.$69.91
D.$106.91

Learn how to calculate the difference between two bank accounts—one with simple interest and the other with compound interest—on a $3,800 deposit over 5 years. This problem covers the formulas for both simple and compound interest, making it ideal for students in Grades 9-12.

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