Numeracy Higher June 2019 Unit 2 Q6
6. Simon has some money to invest in a savings account.
Two banks have sent him details of their Special 1-Year Saver accounts.
He plans to make only one payment into the account and not withdraw any money during the year.
Morgannwg Bank
0·41% interest paid every month
0·41% interest paid every month
Banc Gwynedd
Nominal annual rate of 4·92 %
Interest paid every 3 months
Nominal annual rate of 4·92 %
Interest paid every 3 months
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.
What is the difference between the AERs that the two accounts are offering?
Give your answer as a percentage correct to 2 decimal places. [5]
Difference in AERs = …………………… %
| Scheme | Marks | Comments |
|---|---|---|
| Morgannwg bank 1.004112 – 1 OR \(\left(1+\frac{0.0492}{12}\right)^{12}-1\) | M1 | |
| = 0.0503(…) or 5.03(…)% | A1 | Do not accept 0.0503(…) % unless corrected in further work |
| Banc Gwynedd \(\left(1+\frac{0.0492}{4}\right)^{4}-1\) | M1 | |
| = 0.0501(…) or 5.01(…)% | A1 | Do not accept 0.0501(…) % unless corrected in further work |
| (Answer =) 0.02% | B1 | FT ‘their 0.0503(…) or 5.03(…)%’ AND FT ‘their 0.0501(…) or 5.01(…)%’ provided at least one M1 mark awarded and final answer written correct to 2 d.p |
Alternative
Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| Amount × 1.004112 – amount × \(\left(1+\frac{0.0492}{4}\right)^{4}\) | M2 | M1 for a subtraction with 1 correct product |
| = correct difference | A1 | From M2 only |
| \(\dfrac{\text{difference}}{\text{amount}}\) (× 100) | M1 | FT 'their values' provided at least M1 previously awarded |
| = 0.02% | A1 | Needs to be correct to 2 d.p. on FT |