Percentages: Eduqas GCSE Higher June 2019 Paper 2 Q4

Higher June 2019 Paper 2 Q4

EduqasHigherCurrent spec6 marksPercentages

(a) This motorcycle depreciates by 16% per annum.

Motorcycle now worth £2500

After how many whole years will this motorcycle be worth less than £1000?
You must show all your working. [3]

(b) Rachela takes out a loan for £500 from an online loan company.
The interest rate is 325% per annum.

Rachela is thinking she would pay off the loan and interest in full after 3 years.
A friend correctly says,

“That is a very high rate of interest. You will owe over £30 000.”

Calculate the total amount Rachela would have to pay back after 3 years. [3]

Mark scheme (a)

Scheme	Marks	Comments
\(2500 \times 0.84^n\) with any value of \(n\) from \(n=1\) to \(n=10\) or equivalent	M1	\((2500 \times 0.84 = \text{£}2100)\) \((2500 \times 0.84^2 = \text{£}1764)\) \((2500 \times 0.84^3 = \text{£}1481.76)\) \((2500 \times 0.84^4 = \text{£}1244.6784)\) \((2500 \times 0.84^5 = \text{£}1045.529\ldots)\) \((2500 \times 0.84^6 = \text{£}878.245\ldots)\) \((2500 \times 0.84^7 = \text{£}737.725\ldots)\) \((2500 \times 0.84^8 = \text{£}619.689\ldots)\) \((2500 \times 0.84^9 = \text{£}520.539\ldots)\) \((2500 \times 0.84^{10} = \text{£}437.253\ldots)\)
\(2500 \times 0.84^n\) with a second value of \(n\) from \(n=1\) to \(n=10\) or \(n = 6\) or equivalent leading to an answer closer to £1000 than the previous trial	m1
6 (years)	A1	CAO If no working, award SC2 for an answer of 6 (years)

Mark scheme (b)

Scheme	Marks	Comments
\(500 \times (1 + 325/100)^3\)	M2	M1 for \(500 \times (1 + 325/100)\) (= £2125) or equivalent M1 implied by sight of \(a\times500\times3.25 + b\times500\) or \(a\times1625 + b\times500\), or 5375, or 6375, where \(a \neq 0\) and \(b \neq 0\)
(£) 38 382.81(25)	A1	Accept (£)38382 or 38383 If no marks, award SC1 for sight of \((325/100)^3\) or equivalent or sight of 17164.0625 \((= 3.25^3\times500)\)
	(6)