A lender will loan $183,000 after an 18% down payment. What is the purchase price?

To determine the purchase price based on the loan amount and the down payment percentage, you can use the following calculation method.

First, recognize that the loan amount represents 82% of the total purchase price because a down payment of 18% is required. To find the total purchase price, you can set up the equation where the loan amount ($183,000) equals 82% of the purchase price.

Let ( P ) represent the purchase price. Therefore, you can express it as:

[ 0.82P = 183,000 ]

Next, solve for ( P ) by dividing both sides of the equation by 0.82:

[ P = \frac{183,000}{0.82} ]

Calculating that gives:

[ P = 223,170.73 \approx 223,171 ]

This result confirms that the correct purchase price is approximately $223,171. In summary, understanding the relationship between the loan amount and the percentage of the down payment is key to calculating the total purchase price.