Q85 · Practice questionComplex familiar4 marks
QUESTION 85 (4 marks)
Real GDP grows by 0.5% in each of four consecutive quarters. Use (1 + quarterly growth)^4 − 1 to calculate the compounded annual increase. Explain why multiplying by four gives only an approximation.
WORKED SOLUTION
4 marksPractice marking scheme
Answer
Approximately 2.015% annually, rather than exactly 2%.
Working
(1.005)^4 − 1 = 0.0201505, or 2.01505%. Each quarter’s growth applies to the increased level from the previous quarter. Four times 0.5% omits compounding. This calculation assumes the specified rate in every quarter and should not be confused with an unsupported forecast from one observed quarter.
Marking criteria
- Uses the supplied formula and calculates approximately 2.015%. [2 marks]
- Explains compounding. [1 mark]
- States the relevant assumption/forecast distinction. [1 mark]
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabusHow many marks did you earn?
Compare your working with the guide above.