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Sagot :
Sure, let's break down each step and fill in the missing data.
### Step 1: Calculate the Interest for the Third Month
The balance at the beginning of the third month is \[tex]$366.68. The monthly interest rate is 0.018333. To find the interest charged in the third month (denoted as \( a \)): \[ a = 366.68 \times 0.018333 \] From the result, we know: \[ a = \$[/tex]6.72 \]
### Step 2: Calculate the Payment for the Fourth Month
At the end of the third month, Gary makes another payment of \[tex]$200. This reduces the balance, but we need to include the interest charged on the previous balance before calculating the exact amount paid. The remaining balance after the third month's payment, excluding the fourth month's interest, is: \[ \$[/tex]366.68 - \[tex]$200.00 = \$[/tex]166.68 \]
However, from the provided information, we know the actual fourth month's balance at the start is \[tex]$169.74. Therefore: \[ b = \$[/tex]169.74 \]
### Step 3: Calculate the Interest for the Fourth Month
The balance at the start of the fourth month is \[tex]$169.74. To find the interest charged in the fourth month (denoted as \( c \)): \[ c = 169.74 \times 0.018333 \] From the result, we know: \[ c = \$[/tex]3.11 \]
### Step 4: Calculate the Total Amount Paid by Gary
Gary makes three payments of \[tex]$200 and an adjusted fourth payment, which is the fourth month's balance plus the interest for that month. To sum up, Gary's total payment will include: \[ \text{Three monthly payments } = 3 \times 200 = \$[/tex]600 \]
[tex]\[ \text{Fourth month's payment} = 169.74 + 3.11 = \$172.85 \][/tex]
Adding these amounts together gives us the total amount paid:
[tex]\[ \text{Total amount paid} = 600 + 172.85 = \$772.85 \][/tex]
### Completed Table and Total Amount Paid
Now let’s fill in the table with the calculated values:
\begin{tabular}{|l|c|c|c|}
\hline Balance & Payment & \begin{tabular}{c}
Monthly \\
InterestRate
\end{tabular} & \begin{tabular}{c}
Interest \\
Charged
\end{tabular} \\
\hline[tex]$\$[/tex] 750.00[tex]$ & $[/tex]\[tex]$ 200.00$[/tex] & 0.018333 & [tex]$\$[/tex] 10.08[tex]$ \\ \hline$[/tex]\[tex]$ 560.08$[/tex] & [tex]$\$[/tex] 200.00[tex]$ & 0.018333 & $[/tex]\[tex]$ 6.60$[/tex] \\
\hline[tex]$\$[/tex] 366.68[tex]$ & $[/tex]\[tex]$ 200.00$[/tex] & 0.018333 & [tex]$\$[/tex] 6.72[tex]$ \\ \hline$[/tex]\[tex]$ 169.74$[/tex] & [tex]$\$[/tex] 172.85[tex]$ & 0.018333 & $[/tex]\[tex]$ 3.11$[/tex] \\
\hline
\end{tabular}
So, to summarize:
[tex]\[ a = \$6.72 \][/tex]
[tex]\[ b = \$169.74 \][/tex]
[tex]\[ c = \$3.11 \][/tex]
[tex]\[ \text{Total amount paid by Gary} = \$772.85 \][/tex]
### Step 1: Calculate the Interest for the Third Month
The balance at the beginning of the third month is \[tex]$366.68. The monthly interest rate is 0.018333. To find the interest charged in the third month (denoted as \( a \)): \[ a = 366.68 \times 0.018333 \] From the result, we know: \[ a = \$[/tex]6.72 \]
### Step 2: Calculate the Payment for the Fourth Month
At the end of the third month, Gary makes another payment of \[tex]$200. This reduces the balance, but we need to include the interest charged on the previous balance before calculating the exact amount paid. The remaining balance after the third month's payment, excluding the fourth month's interest, is: \[ \$[/tex]366.68 - \[tex]$200.00 = \$[/tex]166.68 \]
However, from the provided information, we know the actual fourth month's balance at the start is \[tex]$169.74. Therefore: \[ b = \$[/tex]169.74 \]
### Step 3: Calculate the Interest for the Fourth Month
The balance at the start of the fourth month is \[tex]$169.74. To find the interest charged in the fourth month (denoted as \( c \)): \[ c = 169.74 \times 0.018333 \] From the result, we know: \[ c = \$[/tex]3.11 \]
### Step 4: Calculate the Total Amount Paid by Gary
Gary makes three payments of \[tex]$200 and an adjusted fourth payment, which is the fourth month's balance plus the interest for that month. To sum up, Gary's total payment will include: \[ \text{Three monthly payments } = 3 \times 200 = \$[/tex]600 \]
[tex]\[ \text{Fourth month's payment} = 169.74 + 3.11 = \$172.85 \][/tex]
Adding these amounts together gives us the total amount paid:
[tex]\[ \text{Total amount paid} = 600 + 172.85 = \$772.85 \][/tex]
### Completed Table and Total Amount Paid
Now let’s fill in the table with the calculated values:
\begin{tabular}{|l|c|c|c|}
\hline Balance & Payment & \begin{tabular}{c}
Monthly \\
InterestRate
\end{tabular} & \begin{tabular}{c}
Interest \\
Charged
\end{tabular} \\
\hline[tex]$\$[/tex] 750.00[tex]$ & $[/tex]\[tex]$ 200.00$[/tex] & 0.018333 & [tex]$\$[/tex] 10.08[tex]$ \\ \hline$[/tex]\[tex]$ 560.08$[/tex] & [tex]$\$[/tex] 200.00[tex]$ & 0.018333 & $[/tex]\[tex]$ 6.60$[/tex] \\
\hline[tex]$\$[/tex] 366.68[tex]$ & $[/tex]\[tex]$ 200.00$[/tex] & 0.018333 & [tex]$\$[/tex] 6.72[tex]$ \\ \hline$[/tex]\[tex]$ 169.74$[/tex] & [tex]$\$[/tex] 172.85[tex]$ & 0.018333 & $[/tex]\[tex]$ 3.11$[/tex] \\
\hline
\end{tabular}
So, to summarize:
[tex]\[ a = \$6.72 \][/tex]
[tex]\[ b = \$169.74 \][/tex]
[tex]\[ c = \$3.11 \][/tex]
[tex]\[ \text{Total amount paid by Gary} = \$772.85 \][/tex]
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