Foundation November 2024 Paper 3 Q18
18 Darcie invests £\(x\) at a rate of 1.5% per year simple interest for 5 years.
Ivan also invests £\(x\) but at a rate of 1.1% per year simple interest for 6 years.
Darcie earns £108 more interest than Ivan.
Work out the value of \(x\).
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 12 000 with correct working | 6 | Correct working requires evidence of at least 3 M marks | |
| M3 for \(\dfrac{x \times 1.5 \times 5}{100} - \dfrac{x \times 1.1 \times 6}{100} = 108\) oe or better or | Accept any letter for \(x\) e.g. M3 for \(x \times [0].015 \times 5 = x \times [0].011 \times 6 + 108\) or \([0].075x = [0].066x + 108\) | ||
| M1 for \(\dfrac{x \times 1.5 \times 5}{100}\) oe | e.g. \([0].015x \times 5\) or \(\dfrac{7.5x}{100}\) or \(0.075x\) | ||
| M1 for \(\dfrac{x \times 1.1 \times 6}{100}\) oe | e.g. \([0].011x \times 6\) or \(\dfrac{6.6x}{100}\) or \(0.066x\) If both equations seen but only one used allow M1, M1 to stand | ||
| AND M1FT for correctly removing fractions | FT their equation in one variable | ||
| M1FT for correct single \(x\) term isw | e.g. \([0].009x\) [= 108] Note: \([0].075x - [0].066x = 108\) scores M4 | ||
| If 0, 1 or 2 scored, instead award SC3 for answer 12 000 with no or insufficient working | Any calculation of 1.5% or 1.1% of 108 scores 0 See appendix for alternative methods | ||
Appendix
Question 18 Alternative methods
Mark using the one method that leads to the answer
| Method of trials M5 for correct calculation of total interest for both Darcie and Ivan for £12 000 and 108 or correct calculation of total interest for both Darcie and Ivan for an amount other than 12 000 with the interest scaled to 108 or M2 for \(1.5 \times 5\) and \(1.1 \times 6\) or 7.5 and 6.6 or 0.075 and 0.066 or M1 for \(1.5 \times 5\) or \(1.1 \times 6\) or 7.5 or 6.6 or 0.075 or 0.066 | Example using scaling and non calculator methods Guess 5000 Darcie: 1% = 50, 0.5% = 25, 1.5% = 75 Ivan: 1% = 50, 0.1% = 5, 1.1% = 55 Interest = \(75 \times 5 = 375\) \(= 55 \times 6 = 330\) Difference = 45 5000 diff = 45 10 000 diff = 90 1000 diff = 9 90 + 9 + 9 = 108 10 000 + 1000 + 1000 = 12 000 Allow 7.5 and/or 6.6 and 0.075 and/or 0.066 to stand, even if only one is used, unless method abandoned and new begun |
| Numerical method M5 for \(\dfrac{108}{1.5 \times 5 - 1.1 \times 6} \times 100\) oe or M4 for \(\dfrac{108}{1.5 \times 5 - 1.1 \times 6}\) oe or M3 for \(1.5 \times 5 - 1.1 \times 6\) or \(7.5 - 6.6\) or \(0.075 - 0.066\) or M2 for \(1.5 \times 5\) and \(1.1 \times 6\) or 7.5 and 6.6 or 0.075 and 0.066 or M1 for \(1.5 \times 5\) or \(1.1 \times 6\) or 7.5 or 6.6 or 0.075 or 0.066 | Accept 7.5 for \(1.5 \times 5\) and 6.6 for \(1.1 \times 6\) and 0.9 for \(1.5 \times 5 - 1.1 \times 6\) e.g. \(\dfrac{108}{0.009}\) May be implied by 120 or e.g. \(\dfrac{108}{7.5 - 6.6}\) or \(\dfrac{108}{0.9}\) May be implied by 0.9 or 0.009 Allow 7.5 and/or 6.6 and 0.075 and/or 0.066 to stand, even if only one is used, unless method abandoned and new begun |