Question

Gary purchased a $750 TV on a credit card with a 22% annual percentage rate, and he wants to pay it off in payments of $200 per month. The table shows the information for the first four months after Gary used his credit card. A 4-column table with 4 rows. Column 1 is labeled Balance with entries 750 dollars, 560 dollars and 8 cents, 366 dollars and 68 cents, 169 dollars and 74 cents. Column 2 is labeled payment with entries 200 dollars, 200 dollars, 200 dollars, b. Column 3 is labeled Monthly Interest Rate with entries 0.018333, 0.018333, 0.018333, 0.018333. Column 4 is labeled Interest charged with entries 10 dollars and 8 cents, 6 dollars and 60 cents, a, c. Fill in the missing data. a = b = c = What is the total amount Gary will pay?

Answer 1

Gary's interest charged for the third month is $6.72, and for the fourth month is $3.18. The payment for the fourth month, taking into account his remaining balance and interest, is $176.58. The total amount Gary will pay for his TV is $776.58.

Step-by-step explanation:

To fill in the missing data for Gary's credit card payment table, we need to calculate the interest charged each month and determine the payment for the fourth month. Given that the monthly interest rate is 0.018333 (which is the annual rate of 22% divided by 12 months), we can use the formula Interest Charged = Balance × Monthly Interest Rate

For the third month, labeled 'a', we have:

Interest Charged = $366.68 × 0.018333 = $6.72 (rounded to the nearest cent)

Therefore, a = $6.72.

For the fourth month, the payment labeled 'b' is assumed to be another $200. However, we must first check if the remaining balance would be less than $200 after adding the interest from the previous month.

Balance at the start of month 4 = $366.68 (third month balance) - $200 (third month payment) + $6.72 (interest from 'a') = $173.40.

Since $173.40 is less than $200, the payment 'b' would actually be $173.40 plus the interest for the fourth month.

Now, for the fourth month's interest labeled 'c', we have:

Interest Charged = $173.40 × 0.018333 = $3.18 (rounded to the nearest cent)

Thus, payment 'b' is $173.40 + $3.18 = $176.58, and c = $3.18.

To calculate the total amount Gary will pay, we sum up all the payments made over the four months:

Total Payment = $200 + $200 + $200 + $176.58 = $776.58