A buyer makes a 20% down payment and pays two discount points totaling $1,000. What was the purchase price if the loan amount was determined using this information?

To determine the correct purchase price based on the information provided, we first need to understand how the down payment and the points relate to the loan amount.

A down payment of 20% indicates that the loan amount is 80% of the purchase price. Additionally, two discount points, which are each equivalent to 1% of the loan amount, means that the total of $1,000 corresponds to 2% of the loan amount.

Let’s break this down:

1. If $1,000 represents 2% of the loan amount, we can find the loan amount by using the equation:

[

Loan\ Amount = \frac{1000}{0.02} = 50,000

]

2. Given that the loan amount of $50,000 represents 80% of the purchase price, we can find the purchase price by rearranging the formula to find 100% of the purchase price:

[

Purchase\ Price = \frac{Loan\ Amount}{0.80} = \frac{50,000}{0.80} = 62,500

]

This calculation shows that if the loan amount after the down payment is $50