Sure, let's break down the solution step-by-step to determine the amount owed for the installment loan to purchase the patio furniture as described.
1. Initial Information:
- The original price of the patio furniture is [tex]$2600.00.
- There's a discount rate of 20%.
- A down payment of $[/tex]100.00 is required.
2. Calculate the Discount Amount:
To find the discount amount, multiply the original price by the discount rate.
[tex]\[
\text{Discount Amount} = \text{Price} \times \text{Discount Rate}
\][/tex]
Given that the price is [tex]$2600.00 and the discount rate is 20% (or 0.20 in decimal form):
\[
\text{Discount Amount} = 2600.00 \times 0.20 = 520.00
\]
So, the discount amount is $[/tex]520.00.
3. Calculate the New Price after Discount:
Subtract the discount amount from the original price to get the discounted price.
[tex]\[
\text{Discounted Price} = \text{Price} - \text{Discount Amount}
\][/tex]
[tex]\[
\text{Discounted Price} = 2600.00 - 520.00 = 2080.00
\][/tex]
Hence, the discounted price is [tex]$2080.00.
4. Calculate the Amount Owed after Down Payment:
Subtract the down payment from the discounted price to determine the amount owed.
\[
\text{Amount Owed} = \text{Discounted Price} - \text{Down Payment}
\]
\[
\text{Amount Owed} = 2080.00 - 100.00 = 1980.00
\]
Therefore, the amount owed after the down payment is $[/tex]1980.00.
In summary, the discount amount is [tex]$520.00, the new price after the discount is $[/tex]2080.00, and the amount owed after the down payment is [tex]\( \$1980.00 \)[/tex].
