Numeracy Higher November 2020 Unit 2 Q8
8. Imogen has £2000 to invest.
Details of two savings accounts are shown below.
| Account name | Nominal annual rate | Interest paid |
|---|---|---|
| Online Saver | 4·38% | Daily |
| Platinum Plus | 4·5% | Monthly |
(a) If Imogen invested the £2000 in the Online Saver account, how much money would be in the account after 30 days?
You must show all your working. [3]
You must show all your working. [3]
(b) Calculate the AER for the Platinum Plus account.
Give your answer as a percentage correct to 2 decimal places. [3]
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.
Give your answer as a percentage correct to 2 decimal places. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (Amount in account =) \(2000 \times (1 + 0.0438/365)^{30}\) OR \(2000 \times 1.00012^{30}\) | M2 | Allow use of 365.25 or 366 Use of 365.25 leads to 1.0001199… Use of 366 leads to 1.00011967… M1 for 1 error (not omission) e.g.
Note: Use of 12 with a power of 1, instead of 365 with a power of 30, would not be considered as 1 error as it is not of equivalent difficulty, and is M0 |
= (£) 2007.21(…) | A1 | CAO Use of 365.25 leads to (£) 2007.20(7…) Use of 366 leads to (£) 2007.19(…) If no marks awarded, SC1 for answers of:
|
| Scheme | Marks | Comments |
|---|---|---|
| (AER =) \(\left(1 + \dfrac{0.045}{12}\right)^{12} - 1\) | M1 | |
= 4.59 (%) | A2 | A1 for 0.0459(39…%) or 4.59(39…)%, or A1 for 0.046 or 4.6% or 5% from correct working If no marks awarded, SC1 for 4.47 (%) (from use of nominal annual rate of 4.38%. Must be to 2d.p.) |