Let's go through the problem step by step to identify the amount owed for an installment loan to purchase the kitchen appliances.
### Step 1: Calculate the Discount Amount
First, we find the discount amount based on the original price and the given discount percentage.
- Original Price: \[tex]$3200.00
- Discount Percentage: 5%
To calculate the discount, we use the formula:
\[ \text{Discount Amount} = \text{Original Price} \times \left(\frac{\text{Discount Percentage}}{100}\right) \]
Substituting the values:
\[ \text{Discount Amount} = 3200.00 \times \left(\frac{5}{100}\right) \]
\[ \text{Discount Amount} = 3200.00 \times 0.05 \]
\[ \text{Discount Amount} = 160.00 \]
So, the discount amount is \$[/tex]160.00.
### Step 2: Calculate the Price After Discount
Next, we find the price of the kitchen appliances after applying the discount.
[tex]\[ \text{Price After Discount} = \text{Original Price} - \text{Discount Amount} \][/tex]
Substituting the values:
[tex]\[ \text{Price After Discount} = 3200.00 - 160.00 \][/tex]
[tex]\[ \text{Price After Discount} = 3040.00 \][/tex]
So, the price after discount is \[tex]$3040.00.
### Step 3: Calculate the Amount Owed After Down Payment
Finally, we determine the amount that needs to be financed (or owed) by subtracting the down payment from the discounted price.
- Down Payment: \$[/tex]100.00
[tex]\[ \text{Amount Owed} = \text{Price After Discount} - \text{Down Payment} \][/tex]
Substituting the values:
[tex]\[ \text{Amount Owed} = 3040.00 - 100.00 \][/tex]
[tex]\[ \text{Amount Owed} = 2940.00 \][/tex]
So, the amount owed after the down payment is \[tex]$2940.00.
### Summary
The sequence of calculations leads us to:
1. Discount Amount: \$[/tex]160.00
2. Price After Discount: \[tex]$3040.00
3. Amount Owed After Down Payment: \$[/tex]2940.00
Thus, the amount owed for the installment loan to purchase the kitchen appliances after accounting for the discount and down payment is \$2940.00.
