Numeracy Higher June 2025 Unit 2 Q10
10. Menna is going to invest £400 in her bank’s savings account.
The savings account has a special interest rate for one year only.
The account pays 0·2% interest per month for the first 10 months, and then 1·7% interest per month for the last 2 months of the year.
Calculate the AER the bank should be advertising on the account.
Give your answer as a percentage, correct to 2 decimal places. [5]
| Scheme | Mark | Comments |
|---|---|---|
| 400 × \(1.002^{10}\) (=(£)408.07(…)) | M1 | These two M1 marks may be performed in either order |
| × \(1.017^{2}\) | M1 | FT from M0 previously awarded Must be from use of 400 The intermediate answer if done in reverse order is (£)413.71(56) |
| = (£)422.06(…) | A1 | CAO. May be implied in further working |
| (AER =) \(\dfrac{422.06(\ldots) - 400}{400}\) (× 100) OR \(\dfrac{422.06(\ldots)}{400}\) (× 100) − 1 (×100) | M1 | FT ‘their 422.06(…)’ provided it comes from 400 × \(a^{10}\) × \(b^2\) where both a and b are > 1 but < 1.2 |
| = 5.52 (%) | A1 | Must be correct to 2 d.p. If no marks awarded, SC2 for an answer of 5.54 (%) from \(\left(1 + \dfrac{(0.2 \times 10 + 1.7 \times 2)/100}{12}\right)^{12} - 1\) or \(\left(1 + \dfrac{5.4/100}{12}\right)^{12} - 1\) OR SC1 for \(\left(1 + \dfrac{(0.2 \times 10 + 1.7 \times 2)/100}{12}\right)^{12} - 1\) or \(\left(1 + \dfrac{5.4/100}{12}\right)^{12} - 1\) |
Alternative
Alternative method:
| Scheme | Mark | Comments |
|---|---|---|
| \(1.002^{10}\) × \(1.017^{2}\) | M2 | M1 for any one of the following:
|
| = 1.05516(…) | A1 | CAO. May be implied in further working |
| (AER =) (1.05516(…) – 1) ×100 | M1 | FT ‘their 1.05516(…)’ provided it comes from \(a^{10}\) × \(b^2\) where both a and b are > 1 but < 1.2 |
| = 5.52(%) | A1 | Must be correct to 2 d.p. |