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4024/21 May/Jun 2021, Question 1: Compound Interest

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Using Nicole's $22 000 income and $7200 accommodation cost, find percentages, a 4% rise, and compound interest at K% on $2000, showing K = 1.8 and finding complete years to reach $2150.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Calculate what percentage of the $22 000 income the $7200 accommodation spending represents.

  1. 17200/22000 × 100
  2. 2= 32.72…% ≈ 32.7%

Answer32.7 or 32.72 to 32.73

Part (b) · 2 marks

Calculate Nicole's annual income after $22 000 increases by 4%.

  1. 14% of 22 000 = 880
  2. 222 000 + 880 = $22 880

Answer22 880

Part (ci) · 2 marks

Show that the annual compound interest rate K equals 1.8, given $2000 grows to $2036 in one year.

  1. 12000(1 + K/100) = 2036
  2. 21 + K/100 = 2036/2000 = 1.018
  3. 3K = 1.8

Answer2000(1 + K/100) = 2036, leading to (1 + K/100) = 2036/2000 and K = 1.8

Part (cii) · 3 marks

Find how many complete years until the $2000 investment first reaches at least $2150, showing working.

  1. 12000 × 1.018⁴ = 2147.86… < 2150
  2. 22000 × 1.018⁵ = 2186.52… ≥ 2150
  3. 35 years

Answer5

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