Let's examine Mr. Kirov's payment schedule and determine how many more payments he will need to make before his balance reaches [tex]$0.
From the provided table, we know that the balance, after making 3 payments, is \$[/tex]615.70.
Given:
- Initial balance: \[tex]$800
- Monthly payment amount: \$[/tex]100
- Interest rate: 0.012 (1.2% monthly)
The new balance after the first three payments can be calculated as follows:
1. After the first payment:
- Balance: \[tex]$800 - \$[/tex]100 = \[tex]$700
- Interest: \$[/tex]700 * 0.012 = \[tex]$8.40
- New Balance: \$[/tex]700 + \[tex]$8.40 = \$[/tex]708.40
2. After the second payment:
- Balance: \[tex]$708.40 - \$[/tex]100 = \[tex]$608.40
- Interest: \$[/tex]608.40 * 0.012 = \[tex]$7.30
- New Balance: \$[/tex]608.40 + \[tex]$7.30 = \$[/tex]615.70
3. After the third payment:
- Balance: \[tex]$615.70 - \$[/tex]100 = \[tex]$515.70
- Interest: \$[/tex]515.70 * 0.012 = \[tex]$6.19
- New Balance: \$[/tex]515.70 + \[tex]$6.19 = \$[/tex]521.89
Next, we'll continue calculating the balance and number of payments until the balance is less than or equal to zero:
4. After the fourth payment:
- Balance: \[tex]$521.89 - \$[/tex]100 = \[tex]$421.89
- Interest: \$[/tex]421.89 * 0.012 = \[tex]$5.06
- New Balance: \$[/tex]421.89 + \[tex]$5.06 = \$[/tex]426.95
5. After the fifth payment:
- Balance: \[tex]$426.95 - \$[/tex]100 = \[tex]$326.95
- Interest: \$[/tex]326.95 * 0.012 = \[tex]$3.92
- New Balance: \$[/tex]326.95 + \[tex]$3.92 = \$[/tex]330.87
6. After the sixth payment:
- Balance: \[tex]$330.87 - \$[/tex]100 = \[tex]$230.87
- Interest: \$[/tex]230.87 * 0.012 = \[tex]$2.77
- New Balance: \$[/tex]230.87 + \[tex]$2.77 = \$[/tex]233.64
7. After the seventh payment:
- Balance: \[tex]$233.64 - \$[/tex]100 = \[tex]$133.64
- Interest: \$[/tex]133.64 * 0.012 = \[tex]$1.60
- New Balance: \$[/tex]133.64 + \[tex]$1.60 = \$[/tex]135.24
8. After the eighth payment:
- Balance: \[tex]$135.24 - \$[/tex]100 = \[tex]$35.24
- Interest: \$[/tex]35.24 * 0.012 = \[tex]$0.42
- New Balance: \$[/tex]35.24 + \[tex]$0.42 = \$[/tex]35.66
9. After the ninth payment:
- Balance: \[tex]$35.66 - \$[/tex]100 = \$-64.34
At this point, the balance is negative, which means Mr. Kirov has overpaid slightly on his ninth payment. Therefore, no further payments are necessary.
From the start, Mr. Kirov has made a total of 9 payments out of which the first 3 are already accounted for in the table. Hence, the number of additional payments required is:
9 total payments - 3 already made = 6 more payments.
So, Mr. Kirov needs to make 6 more payments before his balance is zero.
The correct answer is
6 payments
