Problem 47
Question
The beginning balance on a bank account is \(\$ 285\). A bank statement shows two deposits: \(\$ 650\) and \(\$ 1324\). It shows many debit card transactions: \(-\$ 39,-\$ 58,-\$ 61\) \(-\$ 475,-\$ 173\), and \(-\$ 81\). Find the new balance in this account. Use negative numbers to represent debits.
Step-by-Step Solution
Verified Answer
The new balance is \$ 1372.
1Step 1 - Add Initial Deposits
Start with the beginning balance of the account, which is \$ 285. Then add the two deposits: \$ 650 and \$ 1324. The equation becomes: \[ 285 + 650 + 1324 \]
2Step 2 - Calculate Total Credits
First add the amounts: \[ 285 + 650 = 935 \] \[ 935 + 1324 = 2259 \] So the total credits are \$ 2259.
3Step 3 - Add Debit Transactions
List all the debit card transactions and add them together: \[ -39 - 58 - 61 - 475 - 173 - 81 \] Which is: \[ -39 - 58 = -97 \] \[ -97 - 61 = -158 \] \[ -158 - 475 = -633 \] \[ -633 - 173 = -806 \] \[ -806 - 81 = -887 \]
4Step 4 - Calculate the New Balance
Subtract the total debits from the total credits to find the new balance: \[ 2259 - 887 = 1372 \] The new balance is \$ 1372.
Key Concepts
addition and subtractionnegative numbersfinancial arithmetic
addition and subtraction
Understanding the concept of addition and subtraction is fundamental in solving financial arithmetic problems. When working with bank account balances, you will frequently add deposits (money going into the account) or subtract debits/withdrawals (money going out of the account).
Addition involves combining values to find a sum. For example, in the given exercise, the bank account starts with a balance of \$ 285\, and then there are deposits of \$ 650\ and \$ 1324\. This means you need to add these amounts: \[ 285 + 650 + 1324 \], which results in a total credit of \$ 2259\.
Subtraction, on the other hand, involves taking away a value from another. In the exercise, after finding the total credits, you have to consider the debits, like \-\$ 39\, \-\$ 58\, etc. These amounts are subtracted from the total credits: \[ 2259 - 887 \].
By mastering addition and subtraction, you can accurately determine your account balance after multiple transactions.
Addition involves combining values to find a sum. For example, in the given exercise, the bank account starts with a balance of \$ 285\, and then there are deposits of \$ 650\ and \$ 1324\. This means you need to add these amounts: \[ 285 + 650 + 1324 \], which results in a total credit of \$ 2259\.
Subtraction, on the other hand, involves taking away a value from another. In the exercise, after finding the total credits, you have to consider the debits, like \-\$ 39\, \-\$ 58\, etc. These amounts are subtracted from the total credits: \[ 2259 - 887 \].
By mastering addition and subtraction, you can accurately determine your account balance after multiple transactions.
negative numbers
Negative numbers play a crucial role in financial arithmetic, especially when dealing with debits or withdrawals from a bank account. Negative numbers are used to represent the reduction in your account balance whenever a debit card transaction occurs.
In the provided exercise, the debits are represented as negative values like \-\$ 39\, \-\$ 58\, etc. To find the total debits, you need to add these negative values. Here’s a step-by-step breakdown:
1. \[ -39 - 58 = -97 \]
2. \[ -97 - 61 = -158 \]
3. \[ -158 - 475 = -633 \]
4. \[ -633 - 173 = -806 \]
5. \[ -806 - 81 = -887 \]
The total debits amount to \-\$ 887\. By understanding how to work with negative numbers, you can correctly interpret the impact of various transactions on your bank balance.
In the provided exercise, the debits are represented as negative values like \-\$ 39\, \-\$ 58\, etc. To find the total debits, you need to add these negative values. Here’s a step-by-step breakdown:
1. \[ -39 - 58 = -97 \]
2. \[ -97 - 61 = -158 \]
3. \[ -158 - 475 = -633 \]
4. \[ -633 - 173 = -806 \]
5. \[ -806 - 81 = -887 \]
The total debits amount to \-\$ 887\. By understanding how to work with negative numbers, you can correctly interpret the impact of various transactions on your bank balance.
financial arithmetic
Financial arithmetic involves calculating the total balance of an account by considering both credits (deposits) and debits (withdrawals). The goal is to maintain a clear picture of the current financial status.
In the given exercise, the starting point is the initial balance of \$ 285\. To find the new balance, follow these steps:
1. **Calculate Total Credits**: Add the deposits like this: \[ 285 + 650 + 1324 = 2259 \].
2. **Calculate Total Debits**: Add the debits (using negative numbers) like this: \[ -39 - 58 - 61 - 475 - 173 - 81 = -887 \].
3. **Determine the New Balance**: Subtract the total debits from the total credits: \[ 2259 - 887 = 1372 \].
The new balance after accounting for all transactions is \$ 1372\. Mastering financial arithmetic allows one to track their financial health accurately by adding all sources of income and subtracting all expenses or debts, giving a clear picture of available funds.
In the given exercise, the starting point is the initial balance of \$ 285\. To find the new balance, follow these steps:
1. **Calculate Total Credits**: Add the deposits like this: \[ 285 + 650 + 1324 = 2259 \].
2. **Calculate Total Debits**: Add the debits (using negative numbers) like this: \[ -39 - 58 - 61 - 475 - 173 - 81 = -887 \].
3. **Determine the New Balance**: Subtract the total debits from the total credits: \[ 2259 - 887 = 1372 \].
The new balance after accounting for all transactions is \$ 1372\. Mastering financial arithmetic allows one to track their financial health accurately by adding all sources of income and subtracting all expenses or debts, giving a clear picture of available funds.