Numeracy Higher June 2017 Unit 2 Q10
10. Fatima wants to invest some money in a savings account.
She has picked up leaflets from two building societies advertising their high-interest savings accounts.
‘Bannau’ account
Nominal annual rate of
3·85%
Interest paid monthly
‘Eryri’ account
Nominal annual rate of
3·86%
Interest paid every
6 months
By comparing AERs, which account will offer Fatima the better interest rate on her investment?
You must show all your working. [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.
| Scheme | Marks | Comments |
|---|---|---|
| Appropriate use of 12 and 2 in the AER formula | B1 | Denominators AND powers |
| Sight of 0∙0385 and 0∙0386 | B1 | Or 3∙85/100 and 3∙86/100 |
| (AER Bannau =) (1+0∙0385/12)12 – 1 OR (AER Eryri =) (1+0∙0386/2)2 – 1 | M1 | |
| (AER Bannau =) 0∙0391(866…) or 0∙0392 OR 3∙91(866…) % or 3∙92 % AND (AER Eryri =) 0∙0389(724…) or 0∙0390 OR 3∙89(724…) % or 3∙9(0) % AND Correct statement e.g. ‘Bannau offers better annual rate of interest’ | A2 | Do not accept 0∙0391(866…)% or 0∙0392% Do not accept 0∙0389(724…)% or 0∙0390% A1 for either correct AER If no marks awarded, SC2 for comparing correct end of year amounts (amount × 1∙0392, amount × 1∙0390) with a correct conclusion SC1 for calculating the correct end of year amount for one account |