the table shows a schedule of mr. kirovs plan for paying off his credit card balance.\nmr. kirovs payment…

the table shows a schedule of mr. kirovs plan for paying off his credit card balance.\nmr. kirovs payment plan\n| balance | payment | new balance | rate | interest || ---- | ---- | ---- | ---- | ---- || $800.00 | $100 | $700.00 | 0.012 | $8.40 || $708.40 | $100 | $608.40 | 0.012 | $7.30 || $615.70 | $100 | $515.70 | 0.012 | $6.19 |if mr. kirov continues to make monthly payments of $100 and does not make any new purchases, how many more payments will he need to make before the balance is 0?○ 4 payments○ 5 payments○ 6 payments○ 7 payments

the table shows a schedule of mr. kirovs plan for paying off his credit card balance.\nmr. kirovs payment plan\n| balance | payment | new balance | rate | interest || ---- | ---- | ---- | ---- | ---- || $800.00 | $100 | $700.00 | 0.012 | $8.40 || $708.40 | $100 | $608.40 | 0.012 | $7.30 || $615.70 | $100 | $515.70 | 0.012 | $6.19 |if mr. kirov continues to make monthly payments of $100 and does not make any new purchases, how many more payments will he need to make before the balance is 0?○ 4 payments○ 5 payments○ 6 payments○ 7 payments

Answer

Explanation:

Step1: Start with current balance

Current balance: $$515.70$

Step2: Calculate 4th payment cycle

  1. Add monthly interest: $515.70 \times 0.012 = 6.19$
  2. New balance before payment: $515.70 + 6.19 = 521.89$
  3. Balance after $$100$ payment: $521.89 - 100 = 421.89$

Step3: Calculate 5th payment cycle

  1. Add monthly interest: $421.89 \times 0.012 \approx 5.06$
  2. New balance before payment: $421.89 + 5.06 = 426.95$
  3. Balance after $$100$ payment: $426.95 - 100 = 326.95$

Step4: Calculate 6th payment cycle

  1. Add monthly interest: $326.95 \times 0.012 \approx 3.92$
  2. New balance before payment: $326.95 + 3.92 = 330.87$
  3. Balance after $$100$ payment: $330.87 - 100 = 230.87$

Step5: Calculate 7th payment cycle

  1. Add monthly interest: $230.87 \times 0.012 \approx 2.77$
  2. New balance before payment: $230.87 + 2.77 = 233.64$
  3. Balance after $$100$ payment: $233.64 - 100 = 133.64$

Step6: Calculate 8th payment cycle

  1. Add monthly interest: $133.64 \times 0.012 \approx 1.60$
  2. New balance before payment: $133.64 + 1.60 = 135.24$
  3. Balance after $$100$ payment: $135.24 - 100 = 35.24$

Step7: Calculate final payment cycle

  1. Add monthly interest: $35.24 \times 0.012 \approx 0.42$
  2. New balance before payment: $35.24 + 0.42 = 35.66$
  3. This balance is less than $$100$, so 1 final payment covers it.

Step8: Count total additional payments

Total cycles needed: 6 (421.89 → 326.95 → 230.87 → 133.64 → 35.24 → 0)

Answer:

6 payments