Why divide by last year index?

Inflation measures change relative to last year, so the rise must be divided by the previous index.

A nominal value ignores price changes; a real value has been deflated by the price index and shows true purchasing power.

S4 Economics Inflation, Paper 1: price index, real wages and purchasing power

2026-11-02

Tutor Prep Guide · Primary English

Ten graded items on the consumer price index, real wage growth, the Fisher relation, a weighted basket and compound real value, each with an answer.

Focus　Divide by the base-year index, deflate nominal values, weight each item and compound across years instead of adding.

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	Four basic, three advanced, two challenge and one error-repair item

02　Questions (10 items)

FoundationThe consumer price index rises from 100 to 108. What is the inflation rate?
FoundationThe price index was 120 last year and is 132 this year. What is this year inflation rate?
FoundationA bag of rice costs $50. If inflation is 6%, what will it cost next year?
FoundationWhat is the definition of inflation?
IntermediateNominal wages rise 5% while inflation is 3%. Find the real wage growth.
IntermediateThe nominal interest rate is 7% and inflation is 4%. Find the real interest rate.
IntermediateA basket is 40% food up 10%, 40% housing up 5% and 20% transport down 2%. Find the weighted inflation rate.
ChallengeInflation is 20% in each of two years. What is the cumulative rise over the two years?
Challenge$1 000 is deposited at 2% compound interest while inflation runs at 3% a year. What is its real value after three years?
Error redoError repair: a student writes that a rising consumer price index means every good has gone up in price. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	8%	The index rises by 8 points, which over the base of 100 is 8%.
2	10%	The 12-point rise must be divided by last year base of 120, which gives 0.10.
3	$53	Multiply by 1.06, so 50 becomes 53.
4	A sustained rise in the general price level	Inflation is a sustained rise in the general price level, not a rise in one good only.
5	About 1.94%	Divide nominal growth by price growth: 1.05 over 1.03 minus 1 gives 0.0194.
6	About 2.88%	Using the exact Fisher relation, 1.07 over 1.04 minus 1 gives 0.0288.
7	5.6%	Weight each change: 0.4 times 10 plus 0.4 times 5 plus 0.2 times minus 2 gives 5.6.
8	44%	Compounding, not adding: 1.2 times 1.2 is 1.44, so 44% over two years.
9	About $971.16	The balance grows to 1 000 times 1.02 cubed, or 1 061.21, and dividing by 1.03 cubed gives 971.16.
10	The index is a weighted average, so individual prices can fall	The index averages a basket, so some items may fall in price while others rise; an average rise does not mean every price rose.

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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