Question

A property sells for $620,000 two years after it was purchased. If the annual appreciation rate was 4%, how much did the original buyer pay for the property (round to the nearest $1,000)?

Answer 1

The original purchase price of the property, after accounting for 4% annual appreciation over two years with a final selling price of $620,000, is approximately $573,000 when rounded to the nearest $1,000.

Step-by-step explanation:

The question involves finding the original price of a property given its final selling price after a period of annual appreciation. To calculate the original purchase price, we need to use the formula for compound appreciation in reverse, known as discounting. Since the appreciation is 4% per year for two years and the final selling price is $620,000, the original purchase price (P) can be found using the formula:

P = Final Price / (1 + rate of appreciation)^number of years

So, substituting the given values, we get:

P = $620,000 / (1 + 0.04)^2

Now, calculate the denominator:

(1 + 0.04)^2 = 1.0816

And then divide by the final price:

P = $620,000 / 1.0816

P = $573,029.94

When rounded to the nearest $1,000, the original purchase price is approximately $573,000.

Answer 2

$574,000

Step-by-step explanation:

To solve this problem you just have to first state how much in percentage of the first place does the final price represents, if the problem tells you that the house is sold 2 years after it was purchased, and it appreciated at a rate of 4% annually, this means that it appreciated 8%, so the total price is actually 108% of the original price, now that we now this we just do a simple rule of three:

`(620,000)/(108)(x)/(100)`

If you clear the rule of three you get:

`x=((620,000)(100))/(108)`

`x=574,074.074`

Since they ask you to round it to the nearest thousand it´d be $574,000