House Price Increase Percentage

[jimjohn123]

can someone plz help me with this question? I keep getting C, but the correct answer is B and I don't get how. thanks in advance!

in a real estate magazine article in 2002, it was stated that the average home in a large metropolitan area was selling for $250,000 and that by 2014 the same house would sell for $500,000. If house prices double in twelve years, what is the average % price increase each year?

A) 4.95%
B) 5.95%
C) 8.33%
D) None of the above

 

[HallsofIvy]

You are calculating "simple interest". You should be doing interest compounded annually.

 

[stapel]

I keep getting C....

How? Please show your work. Thank you!

 

[Ishuda]

First, in test situations like this (or just to get an approximate answer which is generally pretty good), there is a rule of 72 which can be used. That rule is the interest rate times the time is equal to 72 or
i t = 72
So, since t is 12 years, i is about 6%. This would indicate B was the answer (which it is). If I wanted a more accurate answer, I would use a calculator. BTW: had we been given that the interest rate was 6%, the formula would indicate that the time it took to double was about 12 years.

As a hint, we can start with the equation by Denis
(1 + r)¹² = 2
and notice that
1 + r = ( (1 + r)¹² )^(1/12)

 

[Ishuda]

Hmmm....agree Ishuda....but what if the 4 choices had been:
5.9460
5.9463
5.9466
none of above

(1+i)^12 = 2
i = 2^(1/12) - 1 = .059463...

In answer I quote myself: "or just to get an approximate answer which is generally pretty good" and "This would indicate B was the answer (which it is). If I wanted a more accurate answer, I would use a calculator."

So, I would use a calculator.