Problem 51 - Fundamentals of Mathematics

Question

Suppose a person has $$\$ 56$$ in his checking account. He deposits $$\$ 100$$ into his checking account by using the automatic teller machine. He then writes a check for $$\$ 84.50 .$$ If an error causes the deposit not to be listed into this person's account, what is this person's checking bal ance?

Step-by-Step Solution

Answer

The balance is -$28.50.

Step 1: Initial Account Balance

Start with the given initial balance in the checking account, which is $56.

Step 2: Simulate the Deposit Error

Consider the scenario where the deposit of $100 is not added to the account. This means the $100 is not part of the current available balance.

Step 3: Subtract the Check Amount

Deduct the value of the written check, which is \(84.50, from the initial balance of \)56. The calculation is: \[ 56 - 84.50 \].

Step 4: Calculate the New Balance

Now, perform the subtraction: \[ 56 - 84.50 = -28.50 \]. The result indicates a negative balance of $28.50 in the account.

Key Concepts

Understanding Bank Account Balance

Bank account balance refers to the amount of money available in your account at any given time. It is essential to keep track of all transactions to know exactly how much you have remaining.
Balances change with each deposit or withdrawal. For example when money is deposited into the account or payments are made. Keeping an accurate record helps to avoid overdrafts, which occur when you spend more than your available balance. It’s important for personal finance management, ensuring that any checks you write won’t bounce due to insufficient funds. Monitoring your bank account balance regularly is a key practice in managing personal finances effectively.

The Role of Subtraction in Balances

Subtraction plays a critical role in determining your bank account balance, especially when you write checks or make withdrawals. It involves deducting amounts paid out from your initial balance to know how much remains in the account.
For our example, consider you have \( \\(56 \) in your account. If you write a check for \( \\)84.50 \) without a deposit being credited, the balance calculation follows these steps:

• Start with the initial balance: \( \\(56 \).
• Subtract the check amount: \( \\)84.50 \).

The formula used here is:\[Initial\ Balance - Check\ Amount = New\ Balance\]Applying these values gives:\[\\(56 - \\)84.50 = -\$28.50\]This shows how subtraction can result in a negative balance, highlighting the need to ensure funds are sufficient before any payouts.

Handling Financial Errors

Financial error handling is essential to ensure accuracy and prevent potential issues arising from incorrect transactions. Errors, such as missing deposits, can lead to incorrect balance figures. This can result in fees from overdrafts or bounced checks.
To manage such errors effectively, consider the following strategies:

• Regularly check your transaction history to identify discrepancies.
• Immediately report any errors to your bank for prompt correction.
• Keep a personal log of all deposits and withdrawals to reconcile with your bank statements.

Handling financial errors promptly helps maintain trust in your bank and ensures your finances remain in good standing. Developing these habits can save you from potential headaches and financial penalties.