A property sells for $180,000 after one year with a 10% annual appreciation. How much did the original buyer pay?

To determine how much the original buyer paid for the property, we need to reverse the appreciation process. The property appreciated by 10% over the year, meaning that the selling price of $180,000 reflects an increase of 10% from the original purchase price.

To find the original purchase price, we can use the formula for calculating the original price based on the appreciated value. If we let ( P ) represent the original purchase price, we can express the appreciated price as:

[ 180,000 = P + (0.10 \times P) ]

This can be simplified to:

[ 180,000 = 1.10P ]

Now, to find ( P ), we divide both sides by 1.10:

[ P = \frac{180,000}{1.10} ]

Calculating this gives:

[ P = 163,636.36 ]

Rounding this to the nearest dollar, we find that the original buyer paid approximately $163,636. This is why the correct answer is that the original amount paid by the buyer was approximately $163,636.

Understanding this calculation is critical in real estate, especially when analyzing investment returns and property valuations after appreciation.