To solve the question, we need to fill in the missing information in the table based on Gary’s payment schedule and the credit card's annual percentage rate (APR). The APR is 22%, which translates to a monthly interest rate of [tex]\( 0.018333 \)[/tex].
### Month 3:
- The balance at the beginning of month 3 is [tex]\( \$ 366.68 \)[/tex].
- Gary makes a payment of [tex]\( \$ 200.00 \)[/tex].
#### Calculating the interest charged in the third month ([tex]\( a \)[/tex]):
[tex]\[ a = \text{Balance at beginning of month 3} \times \text{Monthly Interest Rate} \][/tex]
[tex]\[ a = 366.68 \times 0.018333 \][/tex]
[tex]\[ a = 6.72 \][/tex]
So, [tex]\( a = \$ 6.72 \)[/tex] (rounded to two decimal places).
### Month 4:
- For month 4, we first need to calculate the remaining balance after Gary’s payment at month 3 and the interest charged.
#### Remaining balance after month 3:
[tex]\[ \text{Remaining balance} = \text{Balance at beginning of month 3} - \text{Payment} + \text{Interest charged} \][/tex]
[tex]\[ \text{Remaining balance} = 366.68 - 200.00 + 6.72 \][/tex]
[tex]\[ \text{Remaining balance} = 173.40 \][/tex]
This remaining balance becomes the balance at the beginning of month 4.
#### Total payment required to completely pay off the balance ([tex]\( b \)[/tex]) in month 4:
[tex]\[ b = \text{Remaining balance} \][/tex]
[tex]\[ b = 173.40 \][/tex]
#### Interest charged in the fourth month ([tex]\( c \)[/tex]):
[tex]\[ c = \text{Remaining balance} \times \text{Monthly Interest Rate} \][/tex]
[tex]\[ c = 173.40 \times 0.018333 \][/tex]
[tex]\[ c = 3.18 \][/tex]
So, [tex]\( c = \$ 3.18 \)[/tex] (rounded to two decimal places).
### Total Payments Made by Gary:
Gary makes three full payments and one partial payment to clear his debt.
- Full payments: [tex]\( 3 \times 200.00 = 600.00 \)[/tex]
- Partial payment: [tex]\( 173.40 \)[/tex]
#### Total payment:
[tex]\[ \text{Total payment} = 600.00 + 173.40 \][/tex]
[tex]\[ \text{Total payment} = 773.40 \][/tex]
### Summary:
- [tex]\( a = \$ 6.72 \)[/tex]
- [tex]\( b = \$ 173.40 \)[/tex]
- [tex]\( c = \$ 3.18 \)[/tex]
- Total amount Gary will pay: [tex]\( \$ 773.40 \)[/tex]
So, the complete filled table looks like this:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Balance} & \text{Payment} & \text{Monthly Interest Rate} & \text{Interest Charged} \\
\hline
\$ 750.00 & \$ 200.00 & 0.018333 & \$ 10.08 \\
\hline
\$ 560.08 & \$ 200.00 & 0.018333 & \$ 6.60 \\
\hline
\$ 366.68 & \$ 200.00 & 0.018333 & \$ 6.72 \\
\hline
\$ 173.40 & \$ 173.40 & -0.018333 & \$ 3.18 \\
\hline
\end{array}
\][/tex]
And the total amount Gary will pay is [tex]\( \$ 773.40 \)[/tex].
