Why divide the index change by the base?

Inflation is the change relative to the base period, so a rise from 120 to 126 is 5%, not 6%.

Why is real interest not simply nominal minus inflation?

Subtraction is only an approximation; the exact method divides by the price ratio, as 1.06 over 1.025 gives 3.41%.

S4 Economics Inflation, Paper 3: index numbers, purchasing power and real interest

2026-11-02

An index change must be divided by the base period, while purchasing power and real interest use ratios and compounding.

Focus　Identify the base and current period first, then decide whether to add, divide or compound.

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 110 to 121. Find the inflation rate.
FoundationFood (weight 40%) rises 5%, housing (40%) rises 2.5% and other items (20%) are unchanged. Find the weighted inflation rate.
FoundationAn item costs $80 and its price rises by 12.5%. Find the new price.
FoundationNominal wages rise 9% while inflation is 5%. Find the change in real wages.
IntermediateThe price index is 150 in year one, 165 in year two and 178.2 in year three. Find the inflation rate in year three.
IntermediateThe nominal interest rate is 6% and inflation is 2.5%. Find the real interest rate.
IntermediateWith inflation at 4% a year, what is $2 000 worth in todays money after two years?
ChallengeA basket costs $400 in the base year and $470 now. Find the cumulative inflation rate and the real value of $1 000 today.
ChallengePrices double every month starting from an index of 100. Find the index after three months and the todays-value purchasing power of $100.
Error redoA student sees the index rise from 120 to 126 and answers 6% inflation. Find the correct rate.

03　Answers and one-line notes

#	Answer	One-line note
1	10%	121 minus 110 is 11, and 11 over the base 110 is 10%.
2	3%	0.4 times 5 is 2 and 0.4 times 2.5 is 1, giving 3%.
3	$90	80 times 1.125 equals 90.
4	About 3.81%	1.09 divided by 1.05, minus 1, gives 3.81%.
5	8%	165 times 1.08 is 178.2, so inflation in the third year is 8%.
6	About 3.41%	1.06 divided by 1.025, minus 1, gives 3.41%.
7	About $1 849.11	2 000 divided by 1.04 squared is 1 849.11.
8	17.5% and about $851.06	70 over 400 is 17.5%, and 1 000 times 400 over 470 is 851.06.
9	800 and $12.50	2 to the power 3 is 8, so 100 times 8 is 800, and 100 over 8 is 12.5.
10	5%	The change of 6 must be divided by the base of 120, which gives 5% rather than 6%.

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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