Answer :
To determine Greg's total balance after making the minimum monthly payment for July, we need to carry out several steps involving the purchases, the monthly interest rate, and the minimum payment rate. We will calculate the balance at the end of each month (after purchases, interest, and payment). Here’s the step-by-step process:
### Step 1: Initial Setup
- Initial balance at the beginning of May: \[tex]$318.97 - APR (annual percentage rate): 11.45% - Monthly interest rate (APR/12): \( 11.45\% / 12 \approx 0.954\% \) or 0.00954 as a decimal. - Minimum payment rate: 2.06% ### Step 2: Monthly Purchases - May Purchases: \$[/tex]46.96, \[tex]$33.51, \$[/tex]26.99
- Total May purchases: \[tex]$46.96 + \$[/tex]33.51 + \[tex]$26.99 = \$[/tex]107.46
- June Purchases: \[tex]$97.24, \$[/tex]112.57
- Total June purchases: \[tex]$97.24 + \$[/tex]112.57 = \[tex]$209.81 - July Purchases: \$[/tex]72.45, \[tex]$41.14, \$[/tex]101.84
- Total July purchases: \[tex]$72.45 + \$[/tex]41.14 + \[tex]$101.84 = \$[/tex]215.43
### Step 3: Calculations for May
1. Add May purchases to the initial balance:
[tex]\[ \text{New Balance} = 318.97 + 107.46 = 426.43 \][/tex]
2. Apply monthly interest:
[tex]\[ \text{Balance with interest} = 426.43 + (426.43 \times 0.00954) = 426.43 + 4.07 \approx 430.50 \][/tex]
3. Calculate minimum payment for May:
[tex]\[ \text{Minimum payment} = 430.50 \times 0.0206 \approx 8.87 \][/tex]
4. Subtract minimum payment from the balance:
[tex]\[ \text{Balance after payment} = 430.50 - 8.87 = 421.63 \][/tex]
### Step 4: Calculations for June
1. Add June purchases to the new balance:
[tex]\[ \text{New Balance} = 421.63 + 209.81 = 631.44 \][/tex]
2. Apply monthly interest:
[tex]\[ \text{Balance with interest} = 631.44 + (631.44 \times 0.00954) = 631.44 + 6.02 \approx 637.46 \][/tex]
3. Calculate minimum payment for June:
[tex]\[ \text{Minimum payment} = 637.46 \times 0.0206 \approx 13.13 \][/tex]
4. Subtract minimum payment from the balance:
[tex]\[ \text{Balance after payment} = 637.46 - 13.13 = 624.33 \][/tex]
### Step 5: Calculations for July
1. Add July purchases to the new balance:
[tex]\[ \text{New Balance} = 624.33 + 215.43 = 839.76 \][/tex]
2. Apply monthly interest:
[tex]\[ \text{Balance with interest} = 839.76 + (839.76 \times 0.00954) = 839.76 + 8.00 \approx 847.76 \][/tex]
3. Calculate minimum payment for July:
[tex]\[ \text{Minimum payment} = 847.76 \times 0.0206 \approx 17.46 \][/tex]
4. Subtract minimum payment from the balance:
[tex]\[ \text{Balance after payment} = 847.76 - 17.46 = 830.31 \][/tex]
### Final Balance
After making the minimum monthly payments for May, June, and July, Greg's total balance on the credit card will be:
\$830.31
### Step 1: Initial Setup
- Initial balance at the beginning of May: \[tex]$318.97 - APR (annual percentage rate): 11.45% - Monthly interest rate (APR/12): \( 11.45\% / 12 \approx 0.954\% \) or 0.00954 as a decimal. - Minimum payment rate: 2.06% ### Step 2: Monthly Purchases - May Purchases: \$[/tex]46.96, \[tex]$33.51, \$[/tex]26.99
- Total May purchases: \[tex]$46.96 + \$[/tex]33.51 + \[tex]$26.99 = \$[/tex]107.46
- June Purchases: \[tex]$97.24, \$[/tex]112.57
- Total June purchases: \[tex]$97.24 + \$[/tex]112.57 = \[tex]$209.81 - July Purchases: \$[/tex]72.45, \[tex]$41.14, \$[/tex]101.84
- Total July purchases: \[tex]$72.45 + \$[/tex]41.14 + \[tex]$101.84 = \$[/tex]215.43
### Step 3: Calculations for May
1. Add May purchases to the initial balance:
[tex]\[ \text{New Balance} = 318.97 + 107.46 = 426.43 \][/tex]
2. Apply monthly interest:
[tex]\[ \text{Balance with interest} = 426.43 + (426.43 \times 0.00954) = 426.43 + 4.07 \approx 430.50 \][/tex]
3. Calculate minimum payment for May:
[tex]\[ \text{Minimum payment} = 430.50 \times 0.0206 \approx 8.87 \][/tex]
4. Subtract minimum payment from the balance:
[tex]\[ \text{Balance after payment} = 430.50 - 8.87 = 421.63 \][/tex]
### Step 4: Calculations for June
1. Add June purchases to the new balance:
[tex]\[ \text{New Balance} = 421.63 + 209.81 = 631.44 \][/tex]
2. Apply monthly interest:
[tex]\[ \text{Balance with interest} = 631.44 + (631.44 \times 0.00954) = 631.44 + 6.02 \approx 637.46 \][/tex]
3. Calculate minimum payment for June:
[tex]\[ \text{Minimum payment} = 637.46 \times 0.0206 \approx 13.13 \][/tex]
4. Subtract minimum payment from the balance:
[tex]\[ \text{Balance after payment} = 637.46 - 13.13 = 624.33 \][/tex]
### Step 5: Calculations for July
1. Add July purchases to the new balance:
[tex]\[ \text{New Balance} = 624.33 + 215.43 = 839.76 \][/tex]
2. Apply monthly interest:
[tex]\[ \text{Balance with interest} = 839.76 + (839.76 \times 0.00954) = 839.76 + 8.00 \approx 847.76 \][/tex]
3. Calculate minimum payment for July:
[tex]\[ \text{Minimum payment} = 847.76 \times 0.0206 \approx 17.46 \][/tex]
4. Subtract minimum payment from the balance:
[tex]\[ \text{Balance after payment} = 847.76 - 17.46 = 830.31 \][/tex]
### Final Balance
After making the minimum monthly payments for May, June, and July, Greg's total balance on the credit card will be:
\$830.31
