CMA Foundation · Fundamentals of Business Mathematics and Statistics · Index Numbers and Time Series
A cost of living index (base 2015 = 100) stands at 160 for 2020. If the base is shifted to 2020 = 100, what will be the index for 2015?
The shifted index for 2015 is 62.50. In base shifting, each old index is divided by the old index of the new base year and multiplied by 100, so 100 divided by 160 times 100 gives 62.5.
- A60.00
- B62.50Correct
- C160.00
- D40.00
Explanation
New index for 2015 = old 2015 index / old 2020 index × 100 = 100/160 × 100 = 62.5. Check: 62.5 × 1.6 = 100. Subtracting 100 − 40 style reasoning giving 60 is wrong because indices change proportionally, not by difference.
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