Numeracy Higher June 2024 Unit 2 Q8
8.
The Cardiff Saver account pays interest at a rate of 0.6% every 3 months.
Evan invests £5000 in this account.
Evan does not make any further deposits or withdrawals after opening the account.
Calculate how much money is in the account after 4\(\frac{1}{2}\) years. [2]
The Pontypridd Saver account has an AER of 4%.
The account pays interest every 6 months.
Myles invests money in this account.
Calculate the interest rate that is applied to the account every 6 months.
Give your answer as a percentage correct to 2 decimal places.
You must show all 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.
| Scheme | Mark | Comments |
|---|---|---|
| 5000 × 1.006\(^{18}\) | M1 | |
| = (£) 5568.44(1446) | A1 | If no marks awarded, SC1 for (5000 × 1.006\(^{17}\) =) (£)5535.23(0…) or (£)5535.23 |
| Scheme | Mark | Comments |
|---|---|---|
| \((1 + x)^2 - 1 = 0.04\) or equivalent | M1 | Allow a place value error in the 0.04 for at most M1m1A0A0 Accept any letter used for x |
| \(1 + x = \sqrt{1.04}\) or equivalent | m1 | |
| x = 0.01(980…) | A1 | |
| (Interest rate every 6 months =) 1.98 (%) | A1 | CAO |
Alternative
8(b) Alternative method:
\(i\) is the nominal annual rate
| Scheme | Mark | Comments |
|---|---|---|
| \(\left(1 + \dfrac{i}{2}\right)^2 - 1 = 0.04\) or equivalent | M1 | Allow a place value error in the 0.04 for at most M1m1A0A0 Accept any letter used for \(i\) |
| \(1 + \dfrac{i}{2} = \sqrt{1.04}\) or equivalent | m1 | |
| \(i\) = 0.03(960…) or 3.96(0…)% | A1 | May be implied in further working If their final answer comes from \(\sqrt{1.04} - 1\) AND 0.03(960…) or 3.96(…)% not seen, then award this A1 for 0.01(980...) or 1.98(03…)(%) rounded or truncated |
| (Interest rate every 6 months =) 1.98 (%) | A1 | CAO |