# maths economics

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• May 22nd 2009, 07:33 AM
jwish
maths economics
hi, can someone please help me with this question, im really struggling with it.
"in a certain location, house prices are decreasing at the rate of 5% per annum. How long will they take to halve? if the rate of inflation is 5%, how long will they take to half in real terms?
• May 22nd 2009, 11:07 AM
HallsofIvy
Quote:

Originally Posted by jwish
hi, can someone please help me with this question, im really struggling with it.
"in a certain location, house prices are decreasing at the rate of 5% per annum. How long will they take to halve? if the rate of inflation is 5%, how long will they take to half in real terms?

100%- 5%= 95% so the value is multiplied by .95 every year. If the original value is V, the value after n years is $0.95^xP$ so you need to solve $0.95^xP= 0.5P$. The "P" cancel and taking logarithms of both sides, x log 0.95= log 0.5 so x= (log 0.95)/(log 0.5).

If inflation is 5%, then the "real" devaluation is 10%. The value of a house is multiplied by 1.00- .10= .90 each year.