CMA Foundation · Fundamentals of Business Mathematics and Statistics · Index Numbers and Time Series
An old index series with base 2010 = 100 ends in 2018 at 150. A new series with base 2018 = 100 shows 120 for 2022. Splicing the new series to the old series, what is the 2022 index on base 2010 = 100?
The spliced 2022 index is 180. The new series value 120 is multiplied by the old series value of 150 for the overlapping year 2018 and divided by 100. This reflects compounding of a 50 percent rise followed by a 20 percent rise.
- A180Correct
- B270
- C170
- D120
Explanation
Spliced index = new index × old index of the linking year / 100 = 120 × 150/100 = 180. Check: prices rose 50% to 2018, then 20% more: 1.5 × 1.2 = 1.8. Adding 50 and 20 to get 170 ignores compounding.
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