Why take a root or a power for multi-year inflation?

Inflation compounds year by year, so a two-year rise of 10.25% is 5% a year, while dividing by two would misstate it.

What does index-linking an allowance achieve?

The cash amount rises but real purchasing power stays the same, since it only restores what prices have taken.

S4 Economics Inflation, Paper 4: compounding, indexation and real income

2026-11-02

Inflation over several years compounds, and allowances and wages must be indexed to the same series before real purchasing power can be compared.

Focus　Separate one-year changes from cumulative changes, then decide whether to root, power or simply divide.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S4 Economics: Inflation
Level	S4

02　Questions (10 items)

FoundationThe consumer price index rises from 250 to 265. Find the inflation rate.
FoundationHousing (weight 50%) rises 4%, food (30%) rises 10% and other items (20%) are unchanged. Find the weighted inflation rate.
FoundationAn item costs $250 and its price is adjusted for 8% inflation. Find the new price.
FoundationNominal wages rise 6% while inflation is also 6%. Find the change in real wages.
IntermediateThe price index is 200 now and 220.5 after two years. Find the average annual inflation rate.
IntermediateNominal income rises from $32 000 to $33 600 while inflation is 8%. Find the change in real income.
IntermediateA monthly allowance of $12 000 is indexed to cumulative inflation of 21% (index 100 to 121). Find the new amount.
ChallengeWith inflation at 3% a year, what is $1 000 worth in todays money after ten years?
ChallengeWages rise 4% a year while inflation is 2.5% a year. Find the cumulative change in real wages after five years.
Error redoThe index rises from 80 to 88 and a student answers 8% inflation. Find the correct rate.

03　Answers and one-line notes

#	Answer	One-line note
1	6%	265 minus 250 is 15, and 15 over the base 250 is 6%.
2	5%	0.5 times 4 is 2 and 0.3 times 10 is 3, giving 5%.
3	$270	250 times 1.08 equals 270.
4	No change, that is 0%	1.06 divided by 1.06 is 1, so real purchasing power is unchanged.
5	5%	220.5 over 200 is 1.1025, and its square root is 1.05, so inflation is 5% a year.
6	A fall of about 2.78%	Income rises 5%, and 1.05 over 1.08 minus 1 gives a fall of 2.78%.
7	$14 520	12 000 times 1.21 is 14 520, which keeps the payment in line with prices.
8	About $744.09	1.03 to the power 10 is 1.3439, and 1 000 over that is 744.09.
9	About 7.53%	1.04 over 1.025 is 1.0146, and its fifth power is 1.0753, a rise of 7.53%.
10	10%	The change of 8 must be divided by the base of 80, which gives 10% rather than 8%.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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