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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

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?

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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.

Why did the vector cross the road?

It wanted to be normal.

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