Higher June 2017 Paper 3 Q16
16 The value of a new car is £18 000
The value of the car decreases by
25% in the first year
12% in each of the next 4 years.
Work out the value of the car after 5 years. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{25}{100} \times 18\,000\) or 4500 and 18 000 – their 4500 or \(18\,000 \times (1 - 0.25)\) or \(18\,000 \times 0.75\) or 13 500 or 0.88 | M1 | oe |
| their \(13\,500 \times (1 - 0.12)^4\) or their \(13\,500 \times 0.88^4\) their \(13\,500 \times (1 - 0.12)^3\) or their \(13\,500 \times 0.88^3\) or 9199.87 or 9199.88 or 9199.90 or 9200 | M1dep | oe Complete method for at least 4 years |
| 8095.88 or 8095.89 or 8095.90 or 8096 or 8096.00 or 8100 or 8100.00 | A1 | Correct money notation |
| Alternative method 2 | ||
| \(\dfrac{25}{100} \times 18\,000\) or 4500 and 18 000 – their 4500 or 13 500 or 0.88 | M1 | oe |
| 13 500, 11 880, 10 454.(…) 9199.(…) | M1dep | oe Complete method for at least 4 years |
| 8095.88 or 8095.89 or 8095.90 or 8096 or 8096.00 or 8100 or 8100.00 | A1 | Correct money notation |
Additional guidance
| Condone eg £8095.88p | M1M1A1 |
| 8095.887… | M1M1A0 |
| Note the values for successive calculations are 13 500, 11880, 10454.4, 9199.87(2), 8095.88(736) The values for successive savings are 4500, 1620, 1425.6, 1254.52(8), 1103.98 | |
| For method marks allow rounding or truncating of their totals or savings |