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.