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
Why this is correct: An index number shows relative change from a base period set to 100. An index of 112 means the current level is 112% of the base, indicating a 12% total increase (112 - 100 = 12). Why the other choices are wrong: 'Prices have risen 112 percent since the base year' misinterprets the index level as the percentage increase. 'Prices have risen 12 percent in each of two years' incorrectly assumes the increase is annual and compounded; the index shows the cumulative change. 'The typical sale price is now $112,000 in that area' is wrong; an index is unitless and does not express a dollar price. Exam tip: To find the total percentage change from an index, subtract 100. An index of 112 means a 12% total increase.
Why This Is the Correct Answer
Option B is correct because subtracting the base of 100 from the current reading of 112 gives a 12 percent total increase since the base year. Equivalently, 112 divided by 100 equals 1.12, which is a 12 percent rise. The statement is properly framed as change since the base year, which matches what a two-period index comparison actually measures. It makes no claim about annual pacing, which the index alone cannot support.
Why the Other Options Are Wrong
Option A: Prices have risen 112 percent since the base year
Reading 112 as a 112 percent increase mistakes the index level for the change, which would imply prices more than doubled. The base of 100 represents the original level, not zero, so the level and the change can never be the same number unless prices doubled to 200. This is the single most common index error and is worth a deliberate check every time.
Option C: Prices have risen 12 percent in each of two years
Twelve percent in each of two years would compound to about 25 percent total, producing an index near 125 rather than 112. The stem gives a cumulative reading, and converting it to an annual rate requires taking the square root of 1.12, roughly 5.8 percent per year. Assuming an annual rate where a cumulative figure was given inflates the change substantially.
Option D: The typical sale price is now $112,000 in that area
An index is unitless by construction, since it is a ratio of one period's level to another's. It carries no information about the absolute dollar level of prices in the market, and two markets with identical indices can have wildly different median prices. Reading an index as dollars confuses a relative measure with an absolute one.
Subtract the Hundred
The base is 100, so the change is whatever sits on top of the hundred. An index of 112 carries 12 above the base, which is 12 percent. An index of 88 sits 12 below, which is down 12 percent. The number itself is a level; the change is what you get after you subtract the hundred.
How to use: First subtract 100 to get the cumulative percentage change. Then ask whether the question wants cumulative or annual, because annual requires taking the appropriate root of the ratio, not dividing by the number of years. If any choice restates the index as dollars, eliminate it immediately since an index has no units.
Exam Tip
To move between two non-base periods, divide the later index by the earlier one; the base of 100 cancels out and you do not need to reference the base year at all.
Common Mistakes to Avoid
- -Reading the index level itself as the percentage change
- -Dividing a cumulative percentage change by the number of years instead of compounding
- -Comparing indices from different services or base years without confirming they are on the same basis
Concept Deep Dive
Analysis
This question tests how to read an index number. An index expresses the level of some measure relative to a base period that is arbitrarily set at 100, so the index value itself is a ratio scaled by one hundred rather than a percentage change or a dollar amount. Reading 112 means the current level is 112 percent of the base, and the change from the base is the index minus 100, or 12 percent cumulative. The word cumulative matters: the 12 percent covers the entire span from the base year to now, and distributing it across the intervening years requires a separate compounding calculation rather than division. Appraisers meet index numbers in cost services, where a local multiplier updates historical construction costs, and in market conditions analysis, where a repeat-sales or median price index supports a time adjustment. In both applications the correct move is the same: compare two index values as a ratio, and convert to a percentage change from that ratio.
Background Knowledge
You need to know that index numbers are relative measures anchored to a base period set at 100, that the change between any two periods equals the ratio of their index values, and that a cumulative change must be converted to an annual rate through compounding rather than division. You should also know where indices appear in practice, including construction cost multipliers and market conditions or time adjustments.
Real-World Application
Updating a construction cost figure from a 2023 estimate, an appraiser applies the cost service's local index, which moved from 214.6 to 231.7. Dividing gives a factor of 1.080, so the historical direct cost is increased by 8.0 percent, and the report documents both index readings and the resulting multiplier.
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