Percentages: WJEC GCSE Numeracy Higher November 2018 Unit 1 Q8

Numeracy Higher November 2018 Unit 1 Q8

WJECHigherCurrent spec10 marksPercentages

8. Cellan is planning to invest a sum of money into a savings account.

Cellan has picked up a leaflet describing an account offered by a local bank.
The details of the account are shown below.

Account name	Minimum term	Minimum investment	Interest paid	Nominal annual interest rate
The Gower	1 year	£1000	Every 6 months	4%

(a)

Calculate the Annual Equivalent Rate (AER) that The Gower account is offering.
Give your answer as a percentage. [5]

From the formula list: Annual Equivalent Rate (AER): AER, as a decimal, is calculated using the formula \(\left(1+\dfrac{i}{n}\right)^{n}-1\), where \(i\) is the nominal interest rate per annum as a decimal and \(n\) is the number of compounding periods per annum.

AER = …………… %

(b)

Give one reason why banks use AER. [1]

(c)

Cellan decides to invest his savings of £3000 into a ‘Gower’ savings account.
He plans to save enough money to buy a motorbike costing £3200.

Calculate how much short of the £3200 Cellan would be after 1 year. [4]

Mark scheme (a)

Scheme	Marks	Comments
Use of 2 as a denominator and power in the AER formula	B1
(AER =) \((1 + 0{\cdot}04/2)^2 - 1\)	M1
Method to calculate 1·02²	m1	For a correct method seen, not for accuracy 1·02 × 1·02 = 1·04 is not sufficient to award this m1 mark
= 0·0404	A1
= 4·04 %	A1	FT from B1M1m1A0 provided their percentage is greater than 4%

Alternative

Alternative method:

Scheme	Marks	Comments
Intention to increase a sum of money by 2%	B1	(e.g. (£)1020)
Correct method to increase a sum of money by 2% twice	M1	(e.g. (£)1040.40)
\(\dfrac{\text{increase}}{\text{original}}\) (× 100 %)	M1	If a candidate uses \(\dfrac{\text{new amount}}{\text{original}}\) (× 100%) do not award M1 unless they then show the intention to subtract 1 (or 100%)
= 0·0404	A1
= 4·04 %	A1	FT from B1M1m1A0 provided their percentage is greater than 4%

Mark scheme (b)

Scheme	Marks	Comments
Explanation e.g. ‘So that customers can compare accounts’, or ‘So that customers (or banks) can compare interest rates accurately’, or ‘Customers (or banks) can easily work out how much they will have after a year’, or ‘To calculate (or show) how much interest they offer per year’	E1	Allow e.g. ‘It’s a higher rate than the nominal annual rate (to make it more attractive)’

Mark scheme (c)

Scheme	Marks	Comments
3000 × 1·0404 OR 3000 × 1·02 × 1·02	M2	FT their AER from part (a) provided of equivalent difficulty M1 for 3000 × 1·02 or equivalent
= (£) 3121.2(0)	A1	FT from M2
(£) 78.8(0)	B1	FT provided M2 awarded AND ‘their (£) 3121.2(0)’ is < (£) 3200 If no marks awarded, and an integer AER derived in (a), then SC1 for 3000 × ‘their 1·0404’ SC2 for the correct evaluated difference between 3200 and 3000 × ‘their 1·0404’