The answer
(a) compounding earns interest on interest
(b) $1250
(c) $219.92
(d) $307.85
O-Level E-Math 2022 Paper 2 Question 2 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 2 of the O-Level E-Math 2022 Paper 2. It tests simple vs compound interest, in the Percentage / Ratio, rate & proportion area. It is worth 11 marks: 1 + 3 + 3 + 4. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
(a) With compound interest each year's interest is added to the balance and itself earns interest in later years, so the total interest after 5 years exceeds the simple-interest total (which only ever pays 1% of the original each year).
(b) Simple interest: amount \(= P(1 + 0.018 \times 6) = 1.108P = 1385 \Rightarrow P = \dfrac{1385}{1.108} = \$1250\).
(c) \(P(1.012)^4 = 4719.92 \Rightarrow P = \dfrac{4719.92}{1.012^4} = \$4500\). Interest \(= 4719.92 - 4500 = \$219.92\).
(d) Fuel used \(= 745 \times \dfrac{5.8}{100} = 43.21\) L; fuel cost \(= 43.21 \times 1.52 = \text{\texteuro}65.68\). Total \(= 134.50 + 65.68 = \text{\texteuro}200.18\). In SGD: \(\dfrac{200.18}{0.66} = \$303.30\), then \(\times 1.015\) (card fee) \(= \$307.85\).
Answer: (a) compounding earns interest on interest
(b) $1250
(c) $219.92
(d) $307.85
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a simple vs compound interest question from Percentage / Ratio, rate & proportion, worth 11 marks: 1 + 3 + 3 + 4.
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