Sure, let's work through the problem step-by-step to find the amount owed for the installment loan.
### 1. Initial Details
- Initial Price of the Home Theater System: \[tex]$3000.00
- Discount Percentage: 10%
- Down Payment: \$[/tex]400.00
### 2. Calculate the Discount Amount
We need to calculate the discount amount given the discount percentage (10%).
[tex]\( \text{Discount Amount} = \frac{\text{Discount Percentage}}{100} \times \text{Initial Price} \)[/tex]
Substituting the given values:
[tex]\( \text{Discount Amount} = \frac{10}{100} \times 3000.00 = 0.1 \times 3000.00 = 300.00 \)[/tex]
So, the discount amount is \[tex]$300.00.
### 3. Calculate the Price After Discount
Now, subtract the discount amount from the initial price to determine the price after the discount.
\( \text{Price After Discount} = \text{Initial Price} - \text{Discount Amount} \)
Substituting the values we have:
\( \text{Price After Discount} = 3000.00 - 300.00 = 2700.00 \)
So, the price after the discount is \$[/tex]2700.00.
### 4. Calculate the Amount Owed After Down Payment
Finally, we subtract the down payment from the price after the discount to find the remaining amount owed.
[tex]\( \text{Amount Owed} = \text{Price After Discount} - \text{Down Payment} \)[/tex]
Substituting the values:
[tex]\( \text{Amount Owed} = 2700.00 - 400.00 = 2300.00 \)[/tex]
So, the amount owed for the installment loan is \$2300.00.
