A house sold for $200,000 in one year and $260,000 ten years later, while the general price level rose 30% over the same period. What does this suggest about its real value?
Correct Answer
B) Real value was about unchanged; the rise was inflation
A dollar change must be read against the change in the general price level. Deflating $260,000 by 1.30 gives about $200,000, so the real value was roughly unchanged; the nominal increase reflects the lower value of money.
Why This Is the Correct Answer
Option B is correct because $260,000 divided by 1.30 equals $200,000, the same as the original price, so the real change is about 0%. The 30% nominal increase reflects the lower value of money, not a gain in real value. Dollar values from different periods must be adjusted for changes in the general price level.
Why the Other Options Are Wrong
Option A: Real value rose about 30% over the ten-year period
Option A is wrong because a real rise of about 30% comes from reporting the nominal change ($260,000 / $200,000 = 1.30) as if it were real. After adjusting for 30% inflation, $260,000 / 1.30 = $200,000, so real value is about unchanged.
Option C: Real value fell about 30% over the ten-year period
Option C is wrong because a real fall of about 30% comes from subtracting inflation twice, taking the 30% inflation away from a price that has only kept pace with it. Deflating correctly, $260,000 / 1.30 = $200,000, which shows no real change.
Option D: Real value rose about 60% over the ten-year period
Option D is wrong because a real rise of about 60% comes from adding the 30% inflation to the 30% nominal change. Inflation should be removed, not added: $260,000 / 1.30 = $200,000, so real value is about unchanged.
Divide out inflation
To find real value, divide the later price by one plus the inflation rate, then compare it with the earlier price.
How to use: Use this whenever a question gives a nominal price change alongside a general price-level change.
Exam Tip
If the nominal change matches the inflation rate, the real change is about zero.
Common Mistakes to Avoid
- -Reporting the nominal increase as a real gain
- -Subtracting inflation twice
- -Adding inflation to the nominal change instead of removing it
Concept Deep Dive
Analysis
This question tests the difference between nominal and real value change. The house rose 30% in dollars, from $200,000 to $260,000, while the general price level also rose 30%. Deflating $260,000 by 1.30 gives $200,000, so the real value is about unchanged.
Background Knowledge
Nominal values are measured in current dollars, while real values adjust for changes in purchasing power. To compare values across time, divide the later value by the price-level index relative to the earlier period. Appraisers use this distinction when interpreting long-term price trends.
Real-World Application
A client is pleased that a rental property sold for 30% more than it cost a decade ago. The appraiser points out that general prices rose by the same 30%, so the property's real value has stayed about the same.
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