A price index for a market is set at 100 in the base year and stands at 112 two years later. What does this show?
Correct Answer
B) Prices have risen 12 percent since the base year
Total index change=(112−100)/100×100=12% over the full two-year period. The current level is 112% of the base, not an increase of 112%. This does not establish 12% per year or a dollar sale price. Subtracting 100 gives the percentage change only when the comparison base is 100; a different base requires division by that base.
Why This Is the Correct Answer
Option B is correct because the change in the index is (112 - 100) / 100 x 100 = 12 percent from the base year to the current reading. That 12 percent describes the total change over the full two-year period. Subtracting 100 gives the percentage change here only because the base is 100.
Why the Other Options Are Wrong
Option A: Prices have risen 112 percent since the base year
Option A says prices have risen 112 percent since the base year. That figure mistakes the index level for the increase; an index of 112 means prices are 112 percent of the base, which is a rise of (112 - 100) / 100 x 100 = 12 percent, not 112 percent.
Option C: Prices have risen 12 percent in each of two years
Option C says prices have risen 12 percent in each of two years. Two successive 12 percent increases would take the index to 100 x 1.12 x 1.12 = 125.44, not 112; the 12 percent is the total change over both years, (112 - 100) / 100 x 100 = 12 percent.
Option D: The typical sale price is now $112,000 in that area
Option D says the typical sale price is now $112,000 in that area. A price index measures relative change from a base and is not stated in dollars, so the reading of 112 does not follow as a $112,000 sale price; it shows only a 12 percent rise from the base, (112 - 100) / 100 x 100.
Index Minus Base, Over Base
Percentage change equals the new reading minus the base reading, divided by the base reading. With a base of 100, 112 becomes 12 over 100, or 12 percent in total.
How to use: Use this formula whenever a question gives two index readings and asks for the change.
Exam Tip
Check whether the question asks for a total change or an annual rate before choosing an answer. If the earlier reading is not 100, divide the difference by that earlier reading rather than simply subtracting.
Common Mistakes to Avoid
- -Reading an index of 112 as a 112 percent increase
- -Treating a total two-year change as an annual rate
- -Interpreting an index number as a dollar sale price
Concept Deep Dive
Analysis
This question tests how to read a price index relative to its base year. The index level of 112 means prices are at 112 percent of the base level, so the total change is (112 - 100) / 100 x 100 = 12 percent over the whole two-year period. The question checks whether candidates confuse the index level with the percentage increase, spread the change across years incorrectly, or treat the index as a dollar price.
Background Knowledge
A price index expresses prices in each period as a percentage of a base period that is set at 100. The percentage change between two readings is the difference divided by the earlier reading. Appraisers use price indexes as one source of evidence about market trends when analyzing time adjustments.
Real-World Application
An appraiser reviewing a regional home price index sees it at 100 two years ago and 112 now. He notes a total rise of about 12 percent over the period, not 12 percent per year. He then compares that trend with paired sales and resales in the subject's market before supporting any time adjustment.
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