Higher June 2022 Paper 4 Q16
16 Li bought a house at the start of 2016.
Li assumes the value of the house, £\(V\), can be predicted using the formula
where \(n\) is the number of years after the start of 2016.
(a) Explain how you know that the value of the house is predicted to increase each year. [1]
(b) Write down the percentage increase per year that is used in the formula. [1]
(c) Write down the value of the house at the start of 2016. [1]
(d) Calculate the predicted value of the house at the start of 2020, giving your answer correct to 4 significant figures. [2]
(e)
(i) Compared with its value at the start of 2016, show that the formula predicts the house will have doubled in value at some point during 2036. [3]
(ii) Give one reason why this may not happen. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 1.035 is greater than 1 oe | 1 | ||
Appendix: exemplar responses for Q16(a)
| Response | Mark |
|---|---|
| 1.035 is above 1 | 1 |
| the percentage multiplier is above 1 | 1 |
| it is being multiplied by a number greater than 1 | 1 |
| the rate is above 1 | 1 |
| the multiplier is higher than 1 | 1 |
| 103.5 means 103.5% and that means 3.5% is added each year | 1(BOD) |
| 103.5% is an increase add on to 100 | 1(BOD) |
| it is above 1 | 1 |
| the number is multiplied by 1 and 3.5% | 1(BOD) |
| the multiplier starts with a 1 | 0 |
| it is being added to 100% | 0 |
| the multiplier is positive | 0 |
| the multiplier is 1.035 | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 3.5 | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 185 000 | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 212 300 | 2 | M1 for \(185\,000 \times 1.035^4\) soi 212 291[. …] If 0 scored B1 for their answer to more than 4 figs correctly rounded to 4 s.f. | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) any correct method, e.g. 368 110[. …] or 368 111 | 2 | M1 for \(185\,000 \times 1.035^{20}\) | Alternate method 1 e.g. \(1.035^{20}\) = 1.98 to 1.99 scores 2 \(1.035^{21}\) = 2.05 to 2.06 scores 1 Alternate method 2 184 055 to 184 056 for 2 marks 190 497 to 190 498 for 1 mark |
| 380 994[. …] or 380 995 | 1 | ||
| (ii) any correct explanation e.g. the rate of increase may not continue | 1 | see appendix | |
Appendix: exemplar responses for Q16(e)(ii)
| Response | Mark |
|---|---|
| the rate of increase may not continue | 1 |
| house prices fluctuate | 1 |
| they could drop | 1 |
| ‘something’ may cause the price to drop (e.g. damage, inflation, local flooding, financial crisis or Brexit) | 1 |
| they may increase at different rates | 1 |
| the house may be demolished | 1 |
| accept any home improvement e.g. extension (might increase faster than predicted) | 1 |
| it is only an estimate | 0 |
| it is only a prediction | 0 |
| house market may have changed | 0 |