QLD Found on Facebook..... (facepalm worthy bad use of maths)

I can't believe how the poster came up with his final conclusion.... 8.74% average growth vs. 9.18% over 24 years....
What's more, other people can't seem to pick it up its not logical. Arrrgghhhh

 

In case you are wondering... Based on the above numbers I got Townsville city had a growth rate of around 4.4% pa over the 24 years whilst Maroubra had 8.7% pa. I.e. Almost double the growth rate....
How can anybody say they are "about the same"?!

Here's what I did to get the above.... Some trial and error.
Take the first years number, take the final years number. Know the number of years growth. Guess the growth rate.
Formula:
starting price x ((1+growth rate)^no. of years of growth) = final price.
The growth rate is the unknown.

This was the trial and error.
153,500 x (1.045^24) = 441,468
278,750 x (1.086^24) = 2,018,973
Keep trying again with better guessed growth rates to get closer numbers....

Overall, I found Maroubra's prices went up around 8.7% per annum over 24 years.
Townsville's went up around 4.4% per annum over 24 years.

 

Maroubra went a bit over 7x initial price, Townsville a little under 3x, I know which I'd prefer to have owned. Something must be screwy with his numbers?

This was interesting from Matusik recently though:

"Over the longer term detached housing resells for similar annual gains regardless of general location (i.e. inner city versus the middle-ring or outer suburbs)."

Matusik Missive: House price growth, Capitals

 

I think while it might have some validity within the city, it doesn't hold true for capital city vs regional centres though.

 

The Townsville median jumped from $319k to $625k from 2015-16.. from 7 sales.. time to stop reading.

 

Yep. That too. Volumes so low it's not reliable

 

I don’t look that closely

 

The returns are compounding (ie: multiply) so using simple averages doesn't work.

Simpler version:
Start with $100K
10% increase one year, followed by a 10% decrease. Simple average = 0% return
So $100K + 10K - 11K = $99K ... an overall loss of $1k

And ... uh, I have forgotten how to solve for x!
Starting with
100(1+x)(1+x)=99
I get down to:
2x + x^2 = -0.01
and I'm stuck ... excel gets me to a real (compounding) average of about -0.5% p.a.

 

Yes. Or starting with 100k. 100% growth followed by a 50% drop gets you back to 100k but the "average" (100% -50%)/2 = 25%. But you have zero growth overall. Huge facepalm.

I think (I did high school ages ago so if i'm wrong....)
Expanding (1+x)^2*100=99
(a^2+2ab+b^2)*100=99
a=1, b=x
(1+2x+x^2)*100=99
1+2x+x^2=99/100
2x+x^2=0.99-1
2x+x^2=-0.01
So I have gotten to the same point as you
I wonder would differentiation help here? (I haven't touched that since first year uni)

Edit: KISS! Lesson.... Don't expand.

(1+x)^2*100=99
(1+x)^2=0.99
Take square roots of both sides
1+x=squareroot(0.99) (*no squareroot symbol here on phone keyboard)
1+x=0.9949874371
x=0.9949874371-1
x= -0.0050125629
Which is -0.501% price shrinkage rate.

But to do for more than 2 years, I couldn't easily get a number (in this calculation I could take a square root but I can't do the same for 24 years of compounding.) So I worked it out using trial and error guesses for the growth rate. See my post #2 in this thread.

 

Truth in your sig ... "Good Teacher"!

 

Uhh... i'll take it as a complement! However for the classes... i'm not the teacher..... (damn)

Let's say I remember high school maths well. (Good teacher in year 11 and 12). And this was definitely some of the maths that stuck.

 

No need to trial and error.. use a scientific calculator
1) Input 24
2) input the function x square root.. (on your computer calculator, its the function left of 4).
3) input 430/143.5
= 1.0438
subtract 1 (formula for compound interest is 1+X)
= 0.0438
= 4.38% annual growth

 

Not that it represents the whole market, but a semi detached 2 bed house next to one I own in the East near Maroubra sold for $35,000 in the late 70s. That's approx a 10% growth rate pa.

 

Scientific calculator on phone is inadequate?

 

CAGR Calculator - Calculate Compound Annual Growth Rate Online
Saves you worrying about forumlas.

 

its on the iphone and on windows calculator..

 

I assumed we all used spreadsheets... do we really calculate this on a calculator?

 

Great! Something simple for the non mathematically inclined to get the number easily....
Thanks so much

Yes, I figured it probably existed... but the calculator I have installed on my phone is a simpler version. Mine doesn't even seem to have the memory buttons

You learn something every day.
Spreadsheet is good for visualising and proving the formula... but if you understand the maths basis of the formula then you don't need the spreadsheet.

 

Rearranging this gives you :

growth rate = ((final price / starting price) ^ (1 / no. of years of growth) - 1

and returns the numbers you got by trial and error below, without the trial and error

 

I think this may work (I also read other websites)