Problem 78 - Elementary Algebra

Question

Suppose a person has $$\$ 56.00$$ in his checking account. He deposits $$\$ 100.00$$ 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 balance?

Step-by-Step Solution

Answer

Answer: The final balance in the person's checking account is -$28.50.

Step 1: Identify the initial balance

The person has an initial balance of $56.00 in their checking account.

Step 2: Account for the deposit not being registered due to the error

Since the error causes the \(100.00 deposit not to be listed, the balance remains at \)56.00.

Step 3: Subtract the written check amount

A check for $84.50 is written, so we will subtract this amount from the current balance to find the final balance: Final Balance = Initial Balance - Check Amount $$ Final Balance = \$56.00 - \$84.50 $$

Step 4: Calculate the final balance

Now we can calculate the final balance after the check is written, taking into account the error: $$ Final Balance = -\$28.50 $$ This person's checking balance is -\$28.50, which indicates an overdraft due to the deposit error.

Key Concepts

Understanding Checking Account Balance

A checking account balance is the amount of money that is currently in your checking account. It is important to keep track of this balance to ensure that you know how much money is available for use. Here’s how it works in practical terms:

• Your balance increases when you deposit money or receive funds.
• It decreases when you withdraw cash or write checks.

In the context of the original exercise, the person initially had a balance of $56.00. This is the starting point for all subsequent transactions. By understanding this, you'll know exactly what is affecting your balance at any given time.

Dealing with Errors in Transactions

An error in a transaction can lead to serious issues like incorrect account balances. These errors could stem from a machine malfunction, human mistakes, or other technical problems. It is crucial to regularly check your account statements to spot any discrepancies as soon as they occur.

For example, in the problem provided, the automatic teller machine (ATM) error led to a missing deposit that should have increased the balance. The deposit of $100 was not recorded due to this error, leaving the balance unchanged. Frequent monitoring can help prevent errors from causing excessive complications.

Calculating Overdraft

Overdraft occurs when more money is withdrawn from an account than what the available balance can cover. This often results in a negative balance, meaning that the account holder owes money back to the bank. Overdraft can lead to extra fees or penalties from the bank if not resolved promptly.

In our solved problem, after writing a check for \(84.50, which was more than the available balance of \)56.00, the account balance dropped to negative $28.50. This is an overdraft situation:
Final Balance: \(56.00 - 84.50 = -28.50\)
To avoid overdraft, keep your balance above zero by meticulously tracking your transactions, enabling you to make informed and responsible financial choices.