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Sagot :
To determine how many more payments Mr. Kirov needs to make before the balance is zero, let's analyze the intermediate balances and interest added each month until the balance is completely paid off. The problem states that he will make monthly payments of [tex]$100, and no new purchases are made with an interest rate of 1.2%.
The initial data and first three entries are given:
- Beginning balance: \$[/tex]800.00
- Monthly payment: \[tex]$100.00 - Interest rate: 1.2% per month The table provides the first three months of payments as follows: | Month | Balance | Payment | Interest Rate | Interest | New Balance | |-------|----------|---------|----------------|-----------|--------| | 1 | \$[/tex]800.00 | \[tex]$100.00 | 0.012 | \$[/tex]8.40 | \[tex]$708.40 | | 2 | \$[/tex]708.40 | \[tex]$100.00 | 0.012 | \$[/tex]7.30 | \[tex]$615.70 | | 3 | \$[/tex]615.70 | \[tex]$100.00 | 0.012 | \$[/tex]6.19 | \[tex]$515.70 | Following the same methodology, let's continue to calculate: #### Month 4: - Previous Balance: \$[/tex]515.70
- Monthly Interest = \[tex]$515.70 * 0.012 = \$[/tex]6.19
- New Balance after Payment = \[tex]$515.70 - \$[/tex]100 + \[tex]$6.19 = \$[/tex]421.89
#### Month 5:
- Previous Balance: \[tex]$421.89 - Monthly Interest = \$[/tex]421.89 * 0.012 = \[tex]$5.06 - New Balance after Payment = \$[/tex]421.89 - \[tex]$100 + \$[/tex]5.06 = \[tex]$326.95 #### Month 6: - Previous Balance: \$[/tex]326.95
- Monthly Interest = \[tex]$326.95 * 0.012 = \$[/tex]3.92
- New Balance after Payment = \[tex]$326.95 - \$[/tex]100 + \[tex]$3.92 = \$[/tex]230.87
#### Month 7:
- Previous Balance: \[tex]$230.87 - Monthly Interest = \$[/tex]230.87 * 0.012 = \[tex]$2.77 - New Balance after Payment = \$[/tex]230.87 - \[tex]$100 + \$[/tex]2.77 = \[tex]$133.64 #### Month 8: - Previous Balance: \$[/tex]133.64
- Monthly Interest = \[tex]$133.64 * 0.012 = \$[/tex]1.60
- New Balance after Payment = \[tex]$133.64 - \$[/tex]100 + \[tex]$1.60 = \$[/tex]35.24
Since the remaining balance after 8 months (approx. \[tex]$35.24) will need another payment, we calculate for the final month: #### Month 9: - Previous Balance: \$[/tex]35.24
- Monthly Interest = \[tex]$35.24 * 0.012 = \$[/tex]0.42
- New Balance after Payment = \[tex]$35.24 - \$[/tex]100 + \[tex]$0.42 = -\$[/tex]64.34
Since the balance is negative after these payments, no further payment is required once the balance crosses zero.
So, Mr. Kirov will need 7 more payments to completely pay off his credit card balance. Therefore, the correct option is:
- 7 payments
- Monthly payment: \[tex]$100.00 - Interest rate: 1.2% per month The table provides the first three months of payments as follows: | Month | Balance | Payment | Interest Rate | Interest | New Balance | |-------|----------|---------|----------------|-----------|--------| | 1 | \$[/tex]800.00 | \[tex]$100.00 | 0.012 | \$[/tex]8.40 | \[tex]$708.40 | | 2 | \$[/tex]708.40 | \[tex]$100.00 | 0.012 | \$[/tex]7.30 | \[tex]$615.70 | | 3 | \$[/tex]615.70 | \[tex]$100.00 | 0.012 | \$[/tex]6.19 | \[tex]$515.70 | Following the same methodology, let's continue to calculate: #### Month 4: - Previous Balance: \$[/tex]515.70
- Monthly Interest = \[tex]$515.70 * 0.012 = \$[/tex]6.19
- New Balance after Payment = \[tex]$515.70 - \$[/tex]100 + \[tex]$6.19 = \$[/tex]421.89
#### Month 5:
- Previous Balance: \[tex]$421.89 - Monthly Interest = \$[/tex]421.89 * 0.012 = \[tex]$5.06 - New Balance after Payment = \$[/tex]421.89 - \[tex]$100 + \$[/tex]5.06 = \[tex]$326.95 #### Month 6: - Previous Balance: \$[/tex]326.95
- Monthly Interest = \[tex]$326.95 * 0.012 = \$[/tex]3.92
- New Balance after Payment = \[tex]$326.95 - \$[/tex]100 + \[tex]$3.92 = \$[/tex]230.87
#### Month 7:
- Previous Balance: \[tex]$230.87 - Monthly Interest = \$[/tex]230.87 * 0.012 = \[tex]$2.77 - New Balance after Payment = \$[/tex]230.87 - \[tex]$100 + \$[/tex]2.77 = \[tex]$133.64 #### Month 8: - Previous Balance: \$[/tex]133.64
- Monthly Interest = \[tex]$133.64 * 0.012 = \$[/tex]1.60
- New Balance after Payment = \[tex]$133.64 - \$[/tex]100 + \[tex]$1.60 = \$[/tex]35.24
Since the remaining balance after 8 months (approx. \[tex]$35.24) will need another payment, we calculate for the final month: #### Month 9: - Previous Balance: \$[/tex]35.24
- Monthly Interest = \[tex]$35.24 * 0.012 = \$[/tex]0.42
- New Balance after Payment = \[tex]$35.24 - \$[/tex]100 + \[tex]$0.42 = -\$[/tex]64.34
Since the balance is negative after these payments, no further payment is required once the balance crosses zero.
So, Mr. Kirov will need 7 more payments to completely pay off his credit card balance. Therefore, the correct option is:
- 7 payments
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