DfE statement R16 · Ratio, proportion and rates of change

Growth and decay, compound interest

part HigherCalculator

Growth and decay, compound interest is content statement R16 of the DfE GCSE mathematics subject content, in the ratio, proportion and rates of change area. It is on both tiers, with a Higher-only part, and it is normally a calculator-paper question. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes." (statement R16). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement R16

Tier

Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "and work with general iterative processes". Everything else in the statement is Foundation content.

Calculator

This is calculator work, which places it on Papers 2 and 3. Know your own calculator before the exam, keep full accuracy through the working and round only at the end.

Common mistakes

Using 0.15 as the multiplier for a 15% decrease. The multiplier is 0.85; 0.15 leaves you with 15% of the amount, not 85%.
Multiplying by the rate n times over rather than raising the multiplier to the power n.
Counting the periods wrong — an investment made at the start of 2020 and valued at the start of 2023 has grown for 3 years, not 4.

Formulae for this statement

Compound interest, growth and decayFinal = P × (1 + r/100)ⁿBe able to derive this

Sample questions (10 of 30)

R16 · Growth and decay, compound interestQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Ratio, proportion and rates of change

R16

Expert

A patient is given a dose of 200 mg of a drug. Each hour, 30% of the drug remaining in the bloodstream is eliminated, and then a further dose of 50 mg is given. Using the recurrence D_{n+1} = 0.7D_n + 50, with D_0 = 200, work out the amount of drug in the bloodstream after 2 hours.

💡 Hints:

Foundation worksheet Higher worksheet Foundation ratio, proportion and rates of change practice Higher ratio, proportion and rates of change practice

Nearby statements

R1Converting between standard and compound units R2Scale factors, scale diagrams and maps R3One quantity as a fraction of another

Questions people ask

Is growth and decay, compound interest on Foundation or Higher?

Both, but not all of it. The parts the DfE prints in bold — "and work with general iterative processes" — are Higher only; the rest is Foundation content.

Can I use a calculator for growth and decay, compound interest?

Yes, on Papers 2 and 3, which are the calculator papers and where questions on this usually sit. Paper 1 is non-calculator.

What is the single most common mistake here?

Using 0.15 as the multiplier for a 15% decrease. The multiplier is 0.85; 0.15 leaves you with 15% of the amount, not 85%.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Ratio, proportion and rates of change at Foundation or at Higher.