CDS (II) 2024 General Knowledge · Question 101 of 120

Correct — D, Cannot be determined. Work out what the series actually gives. From 100 in 2021 to 110 in 2022 the index rises by 10 points on a base of 100, an inflation rate of 10 per cent for 2022. From 110 in 2022 to 132 in 2023 it rises by 22 points on a base of 110, an inflation rate of 20 per cent for 2023. Over the two years together the index rises 32 per cent, but that is cumulative inflation across two years, not an annual rate — the average annual rate over the period is about 14.9 per cent, since 1.10 multiplied by 1.20 equals 1.32. So the data support three different numbers depending on the period chosen, and the question names no period at all. With 10 per cent, 20 per cent and 32 per cent all offered as options and no year specified, the honest reading is that the rate asked for is not determined by the information given.

• (a)10% — This is the rate for 2022 alone, measured from the 2021 base. It is one of several defensible answers, which is what makes it wrong as the answer.
• (b)32% — This is the cumulative rise in the index over two years, not a rate of inflation. Rates compound: 1.10 × 1.20 = 1.32, so 32 per cent is the two-year total, and the average annual rate is about 14.9 per cent.
• (c)20% — This is the rate for 2023, computed correctly as 22/110. It is right for that year only, and the question does not say which year it means.

Inflation is the rate of change of a price index, always computed on the previous period's level. If the index is P0 at the start and P1 at the end, the rate is (P1 − P0)/P0 expressed as a percentage. Because the base moves each year, equal point increases give falling percentage rates and rates over successive years compound rather than add. The base effect is the name for the way a low or high index in the reference period distorts the year-on-year rate.

The arithmetic here is easy; the discipline being tested is reading. Notice that 132 minus 110 is 22 while 110 minus 100 is 10 — the index accelerates. Then notice that the stem asks for 'the rate of inflation' without naming a year, so both 10 per cent and 20 per cent answer it correctly for different years. That is the reason 'cannot be determined' is on the list at all. The main honest caveat is that a reader who assumes the question means the most recent year will answer 20 per cent, and it is worth working out that number too, since a well-posed version of this question would ask for it.

• Inflation rate = (current index − previous index) ÷ previous index × 100.
• Index 100 to 110 gives 10 per cent; 110 to 132 gives 20 per cent, because 22/110 = 0.20.
• Rates compound: 1.10 × 1.20 = 1.32, so the two-year cumulative rise is 32 per cent and the average annual rate is about 14.9 per cent.
• The base effect is the influence of the previous period's index level on the current year-on-year rate.

• Adding annual rates instead of compounding them, which turns 10 and 20 into 30 rather than 32.
• Computing the second year's rate on the original base of 100 and getting 22 per cent.
• Reading a cumulative rise over several years as an annual rate.

As a short numerical on an index series, or as a conceptual item on the base effect and on the difference between headline and core inflation.

• practice — not a real PYQ

  A price index rises from 120 to 138 in a year. The rate of inflation for that year is

  • (a)13%
  • (b)15%
  • (c)18%
  • (d)20%

  Answer(b) 15% — the rise of 18 points is measured on the previous level of 120, and 18/120 = 0.15.

• practice — not a real PYQ

  If inflation is 10 per cent in the first year and 20 per cent in the second, the cumulative rise in the price level over the two years is

  • (a)30%
  • (b)31%
  • (c)32%
  • (d)34%

  Answer(c) 32% — rates compound, so 1.10 × 1.20 = 1.32.