Higher June 2023 Paper 2R Q13
13 Feruzi invests 80 000 Kenyan shillings (KES)
He invests the money for 3 years at \(x\)% compound interest each year.
At the end of 3 years, the total interest he receives is 6151.25 KES
Work out the value of \(x\)
(3)
| Scheme | Marks |
|---|---|
\(80\,000 \times \left(\dfrac{100 + x}{100}\right)^3 = 80\,000 + 6151.25\) oe or \(80\,000 \times \left(1 + \dfrac{x}{100}\right)^3 = 80\,000 + 6151.25\) oe or \(80\,000 \times (1 + x\%)^3 = 80\,000 + 6151.25\) oe or \(80\,000 \times y^3 = 80\,000 + 6151.25\) oe or \(\dfrac{80\,000 + 6151.25}{80\,000}\) (= 1.076…) oe or \(\dfrac{86\,151.25}{80\,000}\) (= 1.076…) oe | M1 |
\(\sqrt[3]{\dfrac{80\,000 + 6151.25}{80\,000}}\) (= 1.025) oe or \(\sqrt[3]{\text{``}1.076\ldots\text{''}}\) (= 1.025) or \(\left(1 + \dfrac{x}{100} = \right)\dfrac{41}{40}\;(= 1.025)\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 2.5 | A1 |
| (3) | |
| (3 marks) |
Notes
A1: Accept answers in the range 2.4 – 2.6 from correct working
NB Do not allow an answer in the range 2.4 – 2.6 if it comes from awrt 7.6% oe or 7.7% oe divided by 3
Do not accept an answer if it is in the range that comes from a simple interest method
(corrected from the printed mark scheme: the Mark column shows 5 for this 3-mark question)