Higher June 2023 Paper 2 Q8
8 Tamsin buys a house with a value of £150 000
The value of Tamsin’s house increases by 4% each year.
Rachel buys a house with a value of £160 000
The value of Rachel’s house increases by 1.5% each year.
At the end of 2 years, whose house has the greater value?
You must show how you get your answer. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| Rachel supported | P1 | for process to begin to work with percentage for year 1 for Tamsin or Rachel, eg \(150000 \times 0.04\ (= 6000)\) oe or \(150000 \times 1.04\ (= 156000)\) oe or \(160000 \times 0.015\ (= 2400)\) oe or \(160000 \times 1.015\ (= 162400)\) oe |
| P1 | for process to use compound interest for Tamsin or Rachel, eg \(\text{``}156000\text{''} \times 0.04\ (= 6240)\) oe or \(\text{``}156000\text{''} \times 1.04\ (= 162240)\) oe or \(\text{``}162400\text{''} \times 0.015\ (= 2436)\) oe or \(\text{``}162400\text{''} \times 1.015\ (= 164836)\) oe or \(1.04^2\ (= 1.0816)\) or \(1.015^2\ (= 1.030225)\) OR for process to begin to work with percentage increase for Tamsin and Rachel for one year, eg \(150000 \times 1.04\ (= 156000)\) oe and \(160000 \times 1.015\ (= 162400)\) oe | |
| P1 | for full process to find figures to compare, eg Tamsin for 2 years and Rachel for 2 years eg \(150000 \times 1.04^2\ (= 162240)\) oe and \(160000 \times 1.015^2\ (= 164836)\) oe OR Tamsin for 2 years and Rachel for 1 year eg \(150000 \times 1.04^2\ (= 162240)\) oe and \(160000 \times 1.015\ (= 162400)\) oe | |
| C1 | for Rachel with supporting figures, eg 162240 and 164836 or 162240 and 162400 or other valid conclusion with supporting comparable figures |
Additional guidance
May be implied by 12000 or 4800 or 162000 or 164800
values may be rounded or truncated to 3 sf
May be implied by 162000 and 164800
Other comparisons are possible
Note that the figure used to compare for Rachel can be the figure after 2 years or after 1 year