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Sagot :
Alright, let's go through the details step-by-step and complete the table using the given information.
We start with:
- An annual percentage rate (APR) of 20%.
- An initial balance of [tex]$600. - Payments and charges for the first and second months. #### Month 1: 1. Initial Balance: \$[/tex]600
2. Payment: \[tex]$400 \[ \text{Balance after payment} = \$[/tex]600 - \[tex]$400 = \$[/tex]200
\]
3. Charges: \[tex]$200 \[ \text{Balance after charges} = \$[/tex]200 + \[tex]$200 = \$[/tex]400
\]
4. Monthly interest rate:
Since the APR is 20%, the monthly interest rate is:
[tex]\[ \text{Monthly interest rate} = \frac{20\%}{12} = \frac{0.20}{12} = 0.0166667 \approx 0.017 \text{ (monthly interest rate)} \][/tex]
5. Interest calculation for the remaining balance before charges:
[tex]\[ \text{Interest} = \text{Balance after payment} \times \text{Monthly interest rate} = \$200 \times 0.0166667 \approx \$3.33 \][/tex]
6. New balance after including interest:
[tex]\[ \text{New balance} = \text{Balance after charges} + \text{Interest} = \$400 + \$3.33 = \$403.33 \][/tex]
#### Month 2:
1. Balance at the start of Month 2: \[tex]$403.33 2. Payment: \$[/tex]300
[tex]\[ \text{Balance after payment} = \$403.33 - \$300 = \$103.33 \][/tex]
3. Charges: \[tex]$100 \[ \text{Balance after charges} = \$[/tex]103.33 + \[tex]$100 = \$[/tex]203.33
\]
4. Interest calculation:
[tex]\[ \text{Interest} = \text{Balance after payment} \times \text{Monthly interest rate} = \$103.33 \times 0.0166667 \approx \$1.72 \][/tex]
5. New balance after including interest:
[tex]\[ \text{New balance} = \text{Balance after charges} + \text{Interest} = \$203.33 + \$1.72 = \$205.06 \][/tex]
Here's the completed table:
| | Amount (in \$) |
|------------------------------|----------------|
| Initial Balance | 600.00 |
| Payment (Month 1) | 400.00 |
| Balance after Payment | 200.00 |
| Charges (Month 1) | 200.00 |
| Balance after Charges | 400.00 |
| Interest (Month 1) | 3.33 |
| Balance after Interest | 403.33 |
| Payment (Month 2) | 300.00 |
| Balance after Payment | 103.33 |
| Charges (Month 2) | 100.00 |
| Balance after Charges | 203.33 |
| Interest (Month 2) | 1.72 |
| Final Balance | 205.06 |
This table represents the updated balances and interest calculations for the given scenario.
We start with:
- An annual percentage rate (APR) of 20%.
- An initial balance of [tex]$600. - Payments and charges for the first and second months. #### Month 1: 1. Initial Balance: \$[/tex]600
2. Payment: \[tex]$400 \[ \text{Balance after payment} = \$[/tex]600 - \[tex]$400 = \$[/tex]200
\]
3. Charges: \[tex]$200 \[ \text{Balance after charges} = \$[/tex]200 + \[tex]$200 = \$[/tex]400
\]
4. Monthly interest rate:
Since the APR is 20%, the monthly interest rate is:
[tex]\[ \text{Monthly interest rate} = \frac{20\%}{12} = \frac{0.20}{12} = 0.0166667 \approx 0.017 \text{ (monthly interest rate)} \][/tex]
5. Interest calculation for the remaining balance before charges:
[tex]\[ \text{Interest} = \text{Balance after payment} \times \text{Monthly interest rate} = \$200 \times 0.0166667 \approx \$3.33 \][/tex]
6. New balance after including interest:
[tex]\[ \text{New balance} = \text{Balance after charges} + \text{Interest} = \$400 + \$3.33 = \$403.33 \][/tex]
#### Month 2:
1. Balance at the start of Month 2: \[tex]$403.33 2. Payment: \$[/tex]300
[tex]\[ \text{Balance after payment} = \$403.33 - \$300 = \$103.33 \][/tex]
3. Charges: \[tex]$100 \[ \text{Balance after charges} = \$[/tex]103.33 + \[tex]$100 = \$[/tex]203.33
\]
4. Interest calculation:
[tex]\[ \text{Interest} = \text{Balance after payment} \times \text{Monthly interest rate} = \$103.33 \times 0.0166667 \approx \$1.72 \][/tex]
5. New balance after including interest:
[tex]\[ \text{New balance} = \text{Balance after charges} + \text{Interest} = \$203.33 + \$1.72 = \$205.06 \][/tex]
Here's the completed table:
| | Amount (in \$) |
|------------------------------|----------------|
| Initial Balance | 600.00 |
| Payment (Month 1) | 400.00 |
| Balance after Payment | 200.00 |
| Charges (Month 1) | 200.00 |
| Balance after Charges | 400.00 |
| Interest (Month 1) | 3.33 |
| Balance after Interest | 403.33 |
| Payment (Month 2) | 300.00 |
| Balance after Payment | 103.33 |
| Charges (Month 2) | 100.00 |
| Balance after Charges | 203.33 |
| Interest (Month 2) | 1.72 |
| Final Balance | 205.06 |
This table represents the updated balances and interest calculations for the given scenario.
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