Asking Price of a House
Date: 10/14/2001 at 20:32:03 From: Helen Carman Subject: Profit on real estate If a seller wants to clear $50,000 for his house and the real estate commission is 6%, what is the formula for the asking price for the house? And what should the asking price for the house be?
Date: 10/15/2001 at 02:01:33 From: Doctor Jeremiah Subject: Re: Profit on real estate Hi Helen, Maybe you just want the answer, but I want to show you how to think about questions like this, so if you will humor me... The asking price equals $50000 + 6% of the asking price. If we write that down in mathematics we get: price = $50000 + 6% of price The tricky part is combining the two "price" terms. We can subtract things from or add things to both sides of the equation, and if we do that with "6% of price" we get: price - 6% of price = $50000 + 6% of price - 6% of price And since "6% of price - 6% of price" equals "0" we get: price - 6% of price = $50000 + 0 price - 6% of price = $50000 But "price" is the same as "100% of price" so we can do this: 100% of price - 6% of price = $50000 And "100% of price - 6% of price" is obviously "94% of price" 94% of price = $50000 Now we need to know the secret of percentages! All percentages work this way: percent means per hundred or "out of 100." Remember that there are 100 cents in a dollar, so 94 percent of a dollar is 0.94, and 94 percent of two dollars is 0.94 times 2. So 94 percent of the asking price is 0.94 times the price: 0.94 x price = $50000 Which we can write as: price x 0.94 = $50000 The tricky part now is combining the two numbers. We can multiply or divide by the same thing on both sides of the equation, and if we do that with 0.94 we get: price x 0.94 / 0.94 = $50000 / 0.94 But 0.94 / 0.94 equals 1, so we get: price x 1 = $50000 / 0.94 And of course, any time we multiply by 1, the 1 just goes away: price = $50000 / 0.94 And that is the price you should ask. Here is how to prove it: price = $53191.49 If the price is $53191.49 and we use our original equation: price = $50000 + 6% of price We get: $53191.49 = $50000 + 6% of $53191.49 We use our percentage secret: $53191.49 = $50000 + 0.06 x $53191.49 And we get: $53191.49 = $50000 + $3191.49 So if you ask $53191.49, then the commission will be $3191.49 and you will end up with $50000 left over. Personally I would ask for $53900 (53.9 thousand) because it's a bit more but it's not quite 54 thousand, which would sound bigger. You know what I mean: everything for sale has a nine at the end of the price. By making it a bit bigger you don't have to get your exact asking price, so if your potential buyers want to haggle you could drop your price by $700 and still get 50 thousand out of it. How much would you get if it did sell for $53900? The formula we ended up with was: asking price = amount you get / 1 minus the commission If the commission is still 6%, then the formula is: asking price = amount you get / .94 If your asking price is $53900, then: $53900 = amount you get / .94 Now remember that we can multiply both sides by anything we want (.94 in this case): .94 x $53900 = .94 x amount you get / .94 And the two .94's on the right side cancel to give: .94 x $53900 = amount you get Which is equal to: $50666 = amount you get Which is a bonus, but most buyers want to get a bargain so don't be surprised if they want to haggle. That's the advantage of setting the price slightly higher. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/
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