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The table shows a schedule of Mr. Kirov's plan for paying off his credit card balance.

\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{4}{|c|}{Mr. Kirov's Payment Plan} \\
\hline Balance & Payment & New Balance & Rate & Interest \\
\hline [tex]$\$[/tex] 800.00[tex]$ & $[/tex]\[tex]$ 100$[/tex] & [tex]$\$[/tex] 700.00[tex]$ & 0.012 & $[/tex]\[tex]$ 8.40$[/tex] \\
\hline [tex]$\$[/tex] 708.40[tex]$ & $[/tex]\[tex]$ 100$[/tex] & [tex]$\$[/tex] 608.40[tex]$ & 0.012 & $[/tex]\[tex]$ 7.30$[/tex] \\
\hline [tex]$\$[/tex] 615.70[tex]$ & $[/tex]\[tex]$ 100$[/tex] & [tex]$\$[/tex] 515.70[tex]$ & 0.012 & $[/tex]\[tex]$ 6.19$[/tex] \\
\hline
\end{tabular}

If Mr. Kirov continues to make monthly payments of [tex]$\$[/tex] 100$ and does not make any new purchases, how many more payments will he need to make before the balance is 0?

A. 4 payments
B. 5 payments
C. 6 payments
D. 7 payments



Answer :

GinnyAnswer
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

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