A buyer makes a 25% down payment on their home. They obtain a loan commitment for $240,000. The purchase price is:
The purchase price is $320,000.
The down payment made by the buyer represents 25% of the total purchase price. Given that the loan commitment is for $240,000, this amount corresponds to the remaining 75% of the purchase price, allowing us to calculate the total purchase price.
If the purchase price were $265,000, a 25% down payment would amount to $66,250, leaving a loan requirement of $198,750 (75% of $265,000). This is significantly less than the loan commitment of $240,000, thus making this option incorrect.
For a purchase price of $300,000, the 25% down payment would be $75,000, resulting in a loan amount of $225,000 (75% of $300,000). While this amount is closer to the loan commitment, it still falls short of the full commitment of $240,000, rendering this option incorrect.
With a purchase price of $320,000, a 25% down payment equals $80,000. The remaining balance, which would need to be financed, is $240,000 (75% of $320,000), perfectly matching the loan commitment. This option is correct as it satisfies all conditions of the problem.
If the purchase price were $345,000, the down payment would be $86,250. This would leave a loan requirement of $258,750 (75% of $345,000), which exceeds the loan commitment of $240,000. Hence, this option is also incorrect.
To determine the purchase price of the home, we recognize that the buyer's loan commitment of $240,000 represents 75% of the total cost. By calculating the total purchase price using the relationship between the down payment and the loan amount, we find that the correct answer is $320,000. This illustrates the importance of understanding how down payments and loan commitments influence total property costs.
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