A deposit of $2,300 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?
A.$287.50
B.$302.24
C.$14.74
D.$147.40

To solve this problem, we need to calculate the final balances for each account after 5 years, then find the difference between the two balances.

### **Account I: Simple Interest**
Simple interest formula:
\[
A = P(1 + rt)
\]
Where:
- $ P = 2300 $ (principal)
- $ r = 2.5\% = 0.025 $ (interest rate)
- $ t = 5 $ years

\[
A_1 = 2300 \times (1 + 0.025 \times 5) = 2300 \times (1 + 0.125) = 2300 \times 1.125 = 2587.50
\]

### **Account II: Compound Interest**
Compound interest formula:
\[
A = P(1 + r)^t
\]
Where:
- $ P = 2300 $ (principal)
- $ r = 0.025 $ (annual interest rate)
- $ t = 5 $ years

\[
A_2 = 2300 \times (1 + 0.025)^5 = 2300 \times (1.025)^5
\]

Let's calculate $ (1.025)^5 $:

\[
A_2 = 2300 \times 1.1314 = 2602.24
\]

### **Difference between the two accounts:**
\[
\text{Difference} = A_2 - A_1 = 2602.24 - 2587.50 = 14.74
\]

Thus, the closest answer is:
\[
\boxed{C. 14.74}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions for practice:
1. What is the future value of an account earning 3% annual simple interest after 4 years with a deposit of $1,500?
2. How does compound interest differ from simple interest over longer periods?
3. What would be the balance if Account II had monthly compounding instead of annual compounding?
4. How would the difference change if the interest rate was 5% instead of 2.5% for both accounts?
5. What is the compound interest earned on a $2,000 deposit after 3 years at 4% interest compounded annually?

**Tip**: Compound interest grows faster than simple interest over time because it earns interest on both the initial principal and previously earned interest!

A deposit of $2,300 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?
A.$287.50
B.$302.24
C.$14.74
D.$147.40

Discover the difference between simple and compound interest with this example of a $2,300 deposit in two accounts over 5 years. Account I uses simple interest, while Account II compounds annually. Learn how to calculate both and determine the final balance and difference, suitable for students in Grades 10-12.

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