Question

ror Analysis  Suppose you have two bank accounts. In Account A you deposit ​$300. In Account B you deposit ​$500. Account A has a simple interest rate of 3.5​%. Account B has a simple interest rate of 2.4​%. One year​ later, you get a bank statement from each bank and one of the statements shows an incorrect amount of interest. The interest for Account A is ​$1 comma 050.00. The interest for Account B is ​$12.00. Which account statement is​ incorrect? Find the​ bank's likely error.
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Part 1
Which account statement is​ incorrect?
A.
Both statements are incorrect.
B.Account Upper B
Account Upper B
C.Account Upper A
Account Upper A

Answer 1

To determine which account statement is incorrect, we need to calculate the correct interest for both accounts based on the given interest rates and the amounts deposited.

### For Account A:
- **Principal (P)** = $300
- **Interest Rate (r)** = 3.5% = 0.035
- **Time (t)** = 1 year

The formula for simple interest (I) is:
\[ I = P \times r \times t \]

Calculating the interest for Account A:
\[
I_A = 300 \times 0.035 \times 1 = 300 \times 0.035 = 10.50
\]

### For Account B:
- **Principal (P)** = $500
- **Interest Rate (r)** = 2.4% = 0.024
- **Time (t)** = 1 year

Calculating the interest for Account B:
\[
I_B = 500 \times 0.024 \times 1 = 500 \times 0.024 = 12.00
\]

### Comparison of Calculated Interest with Statements:
- For **Account A**, the calculated interest is **$10.50** but the statement shows **$1,050.00**. This is a significant discrepancy.
- For **Account B**, the calculated interest is **$12.00** and the statement correctly shows **$12.00**.

### Conclusion:
The incorrect account statement is **Account A**. The likely error in the bank's statement for Account A is that they might have added an extra zero, leading to the incorrect amount of **$1,050.00** instead of the correct **$10.50**.

Thus, the correct answer is:
**C. Account A**