Percentages: WJEC GCSE Numeracy Higher November 2016 Unit 2 Q10

Numeracy Higher November 2016 Unit 2 Q10

WJECHigherCurrent spec11 marksPercentages

10. Huw wants to open a savings account.
Here are the details of savings accounts advertised by two local Welsh banks.

Banc Padarn

Nominal interest rate of 1·98%
per annum

Interest paid monthly

Banc Teilo

AER 1·99%

(a)

(i) What is 1·98% as a decimal?
Circle your answer. [1]

0·0198 0·198 1·098 1·98 98·0

(ii) Which of these two banks should Huw choose in order to gain the most interest per annum?
You must show your working. [4]

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.

(b) Interest earned from savings is taxable, according to the table below.

Tax rates for savings
Basic rate taxpayer	20% on annual interest earned above £1000
Higher rate taxpayer	40% on annual interest earned above £500

Matthew is a higher rate taxpayer.
Therefore, any savings interest he earns over £500 within a year is taxed at 40%.

On 1st May 2016, he invested £150 000 in a savings account that pays interest at a rate of 1·98% per annum.

(i) What is this interest rate per month, written as a decimal?
Circle your answer. [1]

0·0033 0·00495 0·00165 0·0099 0·0066

Savings interest is added at the end of every month.

(ii) Calculate the date when the interest that Matthew earned went above his annual tax-free limit, and the amount of tax he would have to pay on this interest if he had closed the account on this date. [5]

Date ……………………… Tax Matthew would have to pay ………………………

Mark scheme (a)

Scheme	Marks	Comments
(i) 0·0198	B1
(ii) Banc Padarn For use of n = 12 (AER=) (1 + 0·0198/12)¹² – 1 = 0·01998(0…) OR 1·998(0…) %	B1 M1 A1	FT 'their 0·0198' for M1 only Allow 0·02(00..) OR 2(·00) % Do not accept 0·01998 % or 0·02(00..) %
Banc Padarn’s savings account would give most interest per annum.	E1	FT ‘their AER for Banc Padarn’ provided at least M1 awarded AND they are comparing like percentages or decimals Alternative method: B1 for monthly interest rate of 0·00165 M1 for the method of calculating the value of an investment for Banc Padarn after a year (initial investment × 1·00165¹²) and Banc Teilo (initial investment × 1·0199) A1 for accurate values for both banks (with appropriate rounding) E1 for Banc Padarn chosen

Mark scheme (b)

Scheme	Marks	Comments
(i) 0·00165	B1
(ii) (31^st May OR 1^st June) (Interest =) (0·00165 × 150 000) (£)247.5(0)	B1
(30^th June OR 1^st July) (Interest =) (0·00165 × 150 247.5(0)) (£)247.90(84) OR Total interest of (£)495.40(84)	B1	FT ‘their 247.5(0)’
(31^st July OR 1^st August) (Interest =) (0·00165 × 150 495.40(84)) (£)248.31(74) OR Total interest of (£)743.72(58)	B1	FT ‘their 247.90(84)’ Alternative method: B1 for (1·00165×150 000) (£)150247.5(0) B1 for (1·00165²×150 000) (£)150495.40(84) This B1 implies the 1^st B1 B1 for (1·00165³×150 000) (£)150743.72(58) The last B1 implies the previous two B1 marks
(Tax to pay =) (‘their 743.72(58)’ – 500) × 0·4	M1	FT ‘their 743.72(58)’ provided compound interest attempted
31^st July OR 1^st August AND (£)97.49(032)	A1	Allow ‘End of July’ OR ‘30^th July’ for the date Allow (£)97.48 from rounding down of the monthly interest payments