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If the Inflation Rate in 1996 was tripled and the House Price Index was only affected by inflation, what would the House Price Index Outside the Capital be starting in 1997?

 

 

 

 

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Inflation rate (IR) is the average increase in cost or price of goods over a period of time. If something costs x and the rate is r% for the year, the same item a year later costs (1+(r/100))x. The house price index HPI (h) is a number directly proportional to the average rate of change of property prices over a period of time. So if a house price is H in one year and the next year it is H+y, y=kh, where k is the constant of proportionality, so the new price is H+kh.

If 1.5% is tripled it becomes 4.5%, so r=4.5%. A house price of H would be inflated to 1.045H, so kh=0.045.

If r=1.5%=0.015, we know from the table that h=85 in 1996, and in 1997 r=1.6% when h=99, so we should be able to find k.

85k=0.015 or 99k=0.016 if the HPI is only affected by IR, because H goes from H to H+kh=H(1+(r/100)). Therefore, k=0.015/85=3/17000=0.00018, or k=0.016/99=0.00016. These values are different, but it's not clear whether the statement that HPI is only affected by IR applies to the whole HPI table or just to 1996. If we assume the latter, then we take k=0.00018; otherwise we use average k=0.00017. Let's see what difference it makes. For 1996 at triple r, 0.00018h=0.045, making h=0.045/0.00018=250. Using k=0.00017, 0.00017h=0.045, so h=264 and k=0.00016, h=281. These would apply at the beginning of 1997.

The HPI for 1997 (start of year) would be 250 outside the capital, if for 1996 the inflation rate had been 4.5%.

 

by Top Rated User (1.1m points)

If we triple the inflation rate from 1.5 we get an inflation rate of 4.5, represented as 0.045 as a decimal.

We then take the price index in capital from 1996 and multiply it by our inflation rate. 85 x 0.045 = 3.825.

Now we take this number and add it to our original capital index from 1996. 85 + 3.825 = 88.825.

Since we are dealing in dollar points we must round up to the nearest hundredth, making our answer 88.83

by

Using your logic and keeping the rate of inflation at 1.5% instead of tripling it, wouldn't that imply that the HPI would increase by 0.015*85=1.32 making it 85+1.32=86.32? The actual HPI for 1997 is given as 99 which is greater than 86.32 for Outside the Capital. Also, the inflation rate for 2001 is 4.2%, not quite triple 1.5%, and the HPI for 2001 is 211. This seems to imply that the HPI would have been bigger than 211 if the 1996 rate had been tripled.

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