So you've been assigned homework over a topic which has not been covered in class or in the textbook yet? This is not appropriate! And, unfortunately, we cannot here provide the missing hours (or weeks or months) of lesson instruction.
You ask about "any formula I am missing out". Does this mean that you've tried something, and aren't getting the expected result? If so, please reply showing what you've got so far. If not, please clarify this statement.
Either way, what online lessons have you tried, related to "index values"? Thank you!
Stapel
In earlier threads, the OP explained that he is self-reviewing math in preparation for the GRE and he found some sample problems online. So far, each one that I have looked at is poorly worded.
In this case, notice the "year 4-year 5," which makes no sense because there is no such year. A reasonable guess is that means year 4.
Moreover, I can think of at least two ways to do the requested computation, and it is not clear which is intended.
METHOD 1 for year 4:
\(\displaystyle \dfrac{182 - 134(1.016)}{134(1.016)} \approx 33.7\%.\)
This asks what is the difference in the house prices between year 4 and the previous year after adjusting last year's price by what inflation was for the year.
METHOD 2 for year 4:
\(\displaystyle \dfrac{182 - 134}{134} - 0.016\approx 35.8\% - 1.6\% = 34.2\%.\)
But neither of those is suggested as an answer.
So perhaps year 5 was meant.
METHOD 1 for year 5:
\(\displaystyle \dfrac{216 - 182(1.056)}{182(1.056)} \approx 12.4\%.\)
METHOD 2 for year 5:
\(\displaystyle \dfrac{216 - 182}{182} - 0.056\approx 18.7\% - 5.6\% = 13.1\%.\)
But neither of those is suggested as an answer.
What is suggested as an answer is
\(\displaystyle \dfrac{216 - 182}{182} = 18.7\%.\)
That is the percentage change in the nominal price of a house, but it ignores inflation and so is NOT the change in the real price of the house.
They are a TERRIBLE collection of problems.
The OP should stop using them; they are guaranteed to harm his performance on the GRE.
