Question

Greg's January closing balance on his credit card was \(-\$ 1320 .\) In February, he made one payment of \(\$ 450\) and another payment of \(\$ 700 .\) His finance charges were \(\$ 19 .\) Greg made purchases at Tommy's for \(\$ 32\) and Petromart for \(\$ 27 .\) What is his February closing balance?

Short answer

Answer: Greg's February closing balance is -$1242.

Step-by-step solution

Write down Greg's January closing balance

Greg's January closing balance is \(-\$1320\).

Add finance charges to January closing balance

To calculate this, we simply add the finance charges to the January closing balance: \(-\$1320 + \$19 = -\$1301\).

Subtract Greg's payments from the adjusted January closing balance

Greg made one payment of \(\$450\) and another payment of \(\$700\). Subtract these payments from the adjusted January closing balance: \(-\$1301 - \$450 - \$700 = -\$2451 + \$450 + \$ 700 = -\$1301\).

Add Greg's new purchases to the balance

Greg made new purchases of \(\$32\) at Tommy's and \(\$27\) at Petromart. Add these purchases to the previous balance: \(-\$1301 + \$32 + \$27 = -\$1301 + \$59 = -\$1242\).

Write the final answer

Greg's February closing balance after all payments and purchases is \(-\$1242\).

Key concepts

Basic Algebra

Basic algebra involves understanding and manipulating equations to find unknown values. In the context of calculating a credit card balance, algebra is used to apply arithmetic operations such as addition and subtraction to keep track of financial transactions.

For example, to find Greg's February closing balance, we start with his January closing balance and apply a series of algebraic steps. Initially, we have a negative value, \( -\$1320 \), which indicates he owes money. We then adjust this balance by adding and subtracting the various transactions made during February. In algebraic terms, we are solving for the new balance \(x\) with the equation:
\[ x = (-\$1320) + \$19 - \$450 - \$700 + \$32 + \$27. \]
Understanding how to combine like terms (all the charges and credits) and maintaining the correct signs (positive for credits and negative for debits) are key algebraic skills for managing financial equations.

Financial Mathematics

Financial mathematics is a field of applied mathematics that focuses on financial markets and tools, including the management of credit card accounts. In exercises like Greg's balance calculation, financial mathematics helps us understand the impact of payments, charges, and purchases on an account balance.

To properly manage a credit card account, one must take into account payments made towards the balance, any finance charges incurred, and new charges from purchases. The mathematical process involves simple arithmetic but in a financial context. In Greg's situation, we saw that his account was credited with \(\$450\) and \(\$700\) from payments but debited with \(\$19\), \(\$32\), and \(\$27\) due to finance charges and new purchases. It's essential to track each transaction chronologically and apply them correctly to determine the accurate closing balance.

Negative Numbers

In mathematics, negative numbers represent values less than zero, and they are essential to understanding debt and credit relationships in financial contexts such as credit card balances. In Greg's case, his starting balance in January is a negative number, \( -\$1320 \), which signifies that he owes money to the credit card company.

When we add positive numbers (payments and credits) to a negative balance, we are effectively moving closer to zero, or reducing the debt. Subtracting positive numbers (charges) from a negative balance increases the debt, pushing the number further from zero. Conversely, when finance charges are applied to a negative balance, we actually add that charge since charges increase the amount owed, thus making the negative number more significant in magnitude. Through the lens of negative numbers, we can see Greg's transactions shifting his balance from \( -\$1320 \) to \( -\$1242 \) by the end of February after accounting for all his financial activities for the month.