To solve for the missing data in the table and determine the total amount Gary will pay, we need to follow these steps:
1. Find the Interest Charged for the Third Month (a):
For the second month:
- Balance: \[tex]$560.08
- Payment: \$[/tex]200.00
- Monthly Interest Rate: 0.018333
The balance after the second month payment:
[tex]\[
\text{Remaining Balance} = 560.08 - 200.00 = 360.08
\][/tex]
The interest charged for the third month:
[tex]\[
\text{Interest Charged} = 360.08 \times 0.018333 = 6.60
\][/tex]
Therefore, the value of [tex]\( a \)[/tex] (Interest Charged for the third month) is:
[tex]\[
a = 6.60
\][/tex]
2. Confirm the Fourth Month's Payment (b):
For the third month:
- Balance after the monthly payment and interest:
[tex]\[
\text{Balance with Interest (Third Month)} = 360.08 + 6.60 = 366.68
\][/tex]
Payment for the fourth month is already given as [tex]\( \$200.00 \)[/tex]. So in this case, it is correct as:
[tex]\[
b = 200.00
\][/tex]
3. Calculate the Interest for the Fourth Month (c):
The initial balance before the fourth payment:
[tex]\[
366.68 - 200.00 = 166.68
\][/tex]
The interest charged for the fourth month:
[tex]\[
\text{Interest Charged} = 166.68 \times 0.018333 = 3.06
\][/tex]
Therefore, the value of [tex]\( c \)[/tex] (Interest charged for the fourth month) is:
[tex]\[
c = 3.06
\][/tex]
4. Calculate the Total Amount Gary Will Pay:
Gary makes four payments of \[tex]$200 each:
\[
\text{Total Payment} = 4 \times 200.00 = 800.00
\]
To summarize:
- \( a = 6.60 \)
- \( b = 200.00 \)
- \( c = 3.06 \)
- The total amount Gary will pay is \( \$[/tex]800 \).
