- The interest charged each month is calculated using the formula: \(\text{Interest} = (\text{Balance} - \text{Payment}) \times 0.015\).
- Individual monthly interest charges are: \(\$6.00, \$5.34, \$4.6701, \$3.99015, \$3.30,\) and \(\$2.5995\).
- The total interest is the sum of these six values: \(6.00 + 5.34 + 4.6701 + 3.99015 + 3.30 + 2.5995 = 25.89975\).
- Rounded to the nearest cent, the total interest charged is \(\boxed{\$25.90}\).
Explanation
- Understanding the Problem and Formula
The objective is to calculate the total interest charged over a period of 6 months based on the provided credit card payment table. The monthly interest rate is given as \(0.015\). For each month, the interest charged is calculated using the formula:
\[\text{Interest Charged} = (\text{Balance} - \text{Payment}) \times \text{Interest Rate}.\]
We have the balance and payment details for each of the 6 months, and we need to determine the interest for months 2 through 6, then sum these values with the provided interest for month 1.
- Calculating Monthly Interest Charges
Using the formula, we calculate the interest charged for each month:
- Month 1: Given as \(\$6.00\).
- Month 2: \((\$406 - \$50) \times 0.015 = \$356 \times 0.015 = \$5.34\).
- Month 3: \((\$361.34 - \$50) \times 0.015 = \$311.34 \times 0.015 = \$4.6701\).
- Month 4: \((\$316.01 - \$50) \times 0.015 = \$266.01 \times 0.015 = \$3.99015\).
- Month 5: \((\$270 - \$50) \times 0.015 = \$220 \times 0.015 = \$3.30\).
- Month 6: \((\$223.30 - \$50) \times 0.015 = \$173.30 \times 0.015 = \$2.5995\).
- Summing the Interest Charges and Final Answer
Now, we sum all the interest values calculated:
Total Interest = \(\$6.00 + \$5.34 + \$4.6701 + \$3.99015 + \$3.30 + \$2.5995\).
Performing the addition:
- Sum = \(6.00 + 5.34 + 4.6701 + 3.99015 + 3.30 + 2.5995 = 25.89975\).
Rounding the result to the nearest cent, the total interest charged is \(\$25.90\).
Examples
Credit card interest calculations are essential for personal finance management. Understanding how your interest is calculated based on your balance and payments can help you manage your debt more effectively and plan your repayments to minimize interest costs. For example, by knowing how much interest you pay each month, you can decide whether to pay more than the minimum payment to reduce your overall debt faster.