Higher June 2023 Paper 2 Q21
21 Magana decides to put £500 into an account that pays compound interest.
She wants to have at least £560 in the account after 3 years.
Work out to 1 decimal place the minimum annual interest rate she needs. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(560 \div 500\) or 1.12 | M1 | oe |
| \(\sqrt[3]{\text{their } 1.12}\) or [1.038, 1.0385] or [3.8, 3.85] | M1dep | may be implied eg \(\dfrac{r}{100} =\) [0.038, 0.0385] |
| 3.9 | A1 | |
| Alternative method 2 | ||
| Trial of the form \(500 \times x^3\) with \(1 \lt x \leqslant 1.1\) and correct evaluation | M1 | allow correct evaluation truncated or rounded to nearest integer or better allow working year by year value of \(x\) used must be seen |
| Two trials of the form \(500 \times x^3\) each with \(1 \lt x \leqslant 1.1\) and correct evaluations, one with answer \(\lt 560\) and one with answer \(\gt 560\) | M1dep | allow correct evaluations truncated or rounded to nearest integer or better allow working year by year values of \(x\) used must be seen |
| 3.9 | A1 | |
Additional guidance
| Up to M2 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |||||||||||||||||||||||||||
For 578.8125 allow 578, 579, 578.8, 578.81, 578.812, 578.813 | |||||||||||||||||||||||||||
| Alt 2 example of working year by year (allow intermediate values to be truncated or rounded to the nearest penny, also allow if given to the next penny) \(500 \times 1.035 = 517.5\) \(517.5 \times 1.035 = 535.6125\) (allow 535.61 or 535.62) \(535.61 \times 1.035 = 554.35635\) | |||||||||||||||||||||||||||
| Incorrect trials and evaluations can be ignored | |||||||||||||||||||||||||||
| 3.9 from incorrect working eg \(560 - 500 = 60 \qquad \sqrt[3]{60} = 3.9\) | M0M0A0 | ||||||||||||||||||||||||||
| Wrong answer (eg 4) with no correct method seen | M0M0A0 | ||||||||||||||||||||||||||
| Apply the scheme that favours the student eg \(500 \times 1.038^3\) scores M1M1 using Alt 1 | |||||||||||||||||||||||||||
| \(\dfrac{560 - 500}{500}\) with no further correct work | M0M0 |