# Basic Algebra help

• Feb 15th 2013, 10:40 AM
ROCKCDXX
Basic Algebra help
I'm taking a real estate course and brushing up on my math. I'm doing a practice test from my book and this problem has me stumped, and there's no explanation for it in the book.

The value of a house today is \$37,500. It has been depreciating (losing value) 2.5% per year. What was the value of the house 10 years ago?

So as I understand it the equation should look like: x-(x0.025(10)=37,500

which breaks down to x-x0.25=37,500

or x minus 25% of x equals 37,500 if I'm not writing it correctly above... Am I right so far? How do I finish this?
• Feb 15th 2013, 10:48 AM
sakonpure6
Re: Basic Algebra help
If the house costs 37500 now and it is depreciating 2.5 % every year, then to find it's value 10 years ago we need to increase the property value which is 37500 by 2.5 % for 10 years and the equation to solve this would be (1+0.025)^10(37500). We do (1+0.025) because we are increasing the value by 2.5 percent. The 10 is the number of years ( it is also the x variable).

the answer is about \$48003 and you can check this by depreciating this value by 2.5% for 10 years which will give your initial house value of \$37500
• Feb 15th 2013, 10:53 AM
ROCKCDXX
Re: Basic Algebra help
2.5% of the original value is not the same as 2.5% of the current value... the answer should be \$50000 I believe, but I don't know how to get there...
• Feb 15th 2013, 10:56 AM
sakonpure6
Re: Basic Algebra help
Quote:

Originally Posted by ROCKCDXX
2.5% of the original value is not the same as 2.5% of the current value... the answer should be \$50000 I believe, but I don't know how to get there...

if it is loosing 2.5% every year, then if you go back in time, the price should also increase 2.5% every year.
• Feb 15th 2013, 11:00 AM
ROCKCDXX
Re: Basic Algebra help
right but by 2.5% of the unknown number
• Feb 15th 2013, 11:01 AM
sakonpure6
Re: Basic Algebra help
??

value of property 10 years ago= (1.025)^10years (property value now)
• Feb 15th 2013, 11:15 AM
ROCKCDXX
Re: Basic Algebra help
Never mind I figured it out... for future reference, knowing the house has depreciated 25% over 10 years, 37500 represents 75% of the original value... 37,500/75%= 50,000... thanks for the help anyway
• Feb 16th 2013, 03:31 AM
ibdutt
Re: Basic Algebra help
You need to use the formula for Compound interest i.e., A = P ( 1 + r/100)^n, where A is amount, P - principal, r rate and n time. In this case we will have to take rate as negative since it is depreciation.