Math Is Fun Forum

careless25

Real Member

Registered: 2008-07-24

Posts: 560

Avg rate of change and percentage

Real estate often increases in value overtime. A parcel of land is purchased for $35000. After 9 years, the land is sold for $51000. What is the average annual rate of change in the value of the real estate, as a percentage?

I get average rate of change as $1777.78. I am not sure about the percentage though.
I did (51000/35000)/9years* 100.
i get 16.2%
Is that correct?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Avg rate of change and percentage

You've started well by dividing the final amount by the start amount to get a percentage.
But instead of dividing this by 9, you need to take the 9th root.

It turns out that the land increases in value by ~4.27% each year.

ie.
After year 1, it is 35000 * 1.042 = 36495
After year 2, it is 36495 * 1.042 = 38054
...

This way is more natural, because the increase is dependent on whatever the value is at the time, rather than what it started as.

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Why did the vector cross the road?
It wanted to be normal.