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# What is the house worth now?

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A house purchased for \$226,000 has lost 3% of its value each year for the past 5 years.

What is the house worth now?

Feb 23, 2019

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okay so first we divide the house's original value by 100, We end up with 2,260 then multiply this number by fifteen ( since the house's lose's three percent in value every year we multiply three by the number of years. which in turn we end up with 33,900 then we sub stubtract this from the original value and we get \$192,100

Feb 23, 2019
edited by HiylinLink  Feb 23, 2019
#2
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I don't see this as straight line deductions.  I see the house losing less each year because it is worth less each year.

Lets call 226,000 by the letter V (for Value) simply so we don't have to juggle that long number repeatedly.

At the end of the 1st year, the house has lost 3% of V so its remaining worth is (0.97)V

At the end of the 2nd year, the house has lost 3% of (0.97)V so it is now worth (0.97)(0.97)V

At the end of the 3rd year, the house has lost 3% of (0.97)(0.97)V so now its worth is (0.97)(0.97)(0.97)V

At the end of the 4th year, the house has lost 3% of (0.97)(0.97)(0.97)V so now it's worth (0.97)(0.97)(0.97)(0.97)V

At the end of the 5th year, the house has lost 3% of (0.97)(0.97)(0.97)(0.97)V and is worth (0.97)(0.97)(0.97)(0.97)(0.97)V

You can see where this is going.  It's an exponential function.  Anyway, let's just do the arithmetic now.

0.97 x 0.97 x 0.97 x 0.97 x 0.97 x \$226,000 =  \$194,073.89

Another way to write this would be (0.97)5 x \$226,000 =  \$194,073.89

Feb 23, 2019
#3
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The Guest is correct:

FV = PV x [1 + R]^N

FV =\$226,000 x [1 - 3%]^5

FV =\$226,000 x [0.97]^5

FV =\$226,000 x   0.8587340257

FV =\$194,073.89 - what the house will be worth in 5 years.

Feb 23, 2019