Higher November 2019 Paper 1 Q5
5.
(a) Delyth borrows £3450 from a family member who charges her 2% per year simple interest.
She pays all the money back in one payment after 1 year 3 months.
How much interest does Delyth pay? [3]
She pays all the money back in one payment after 1 year 3 months.
How much interest does Delyth pay? [3]
(b) Aiden invested £65 for 5 years at a rate of \(r\)% simple interest per year.
No extra money was paid in and no money was withdrawn during these 5 years.
At the end of the 5 years he received £9.75 interest in total.
Find the value of \(r\). [3]
No extra money was paid in and no money was withdrawn during these 5 years.
At the end of the 5 years he received £9.75 interest in total.
Find the value of \(r\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(34.50 \times 2 + (34.50 \times 2) \div 4\) oe si | M2 | e.g. for 69 + 17.25 or \(\dfrac{3450 \times 2 \times 1\frac{3}{12}}{100}\) or \(\dfrac{3450 \times 2\frac{1}{2}}{100}\) oe M1 for \(34.50 \times 2\) oe si or for \(3450 \times 1.02 - 3450\) \((= 3519 - 3450)\) or for sight of (£)69 or for sight of 2.5% oe |
| (£)86.25 | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{65 \times r \times 5}{100} = 9.75\) or \(\dfrac{65 \times r}{100} = \dfrac{9.75}{5}\) or 1.95 (per year interest) oe | M1 | |
| \((r =)\ \dfrac{9.75 \times 100}{5 \times 65}\) oe | M1 | e.g. \(\dfrac{1.95}{65} \times 100\) or sight of \(\dfrac{3}{100}\) |
| 3 ISW | A1 | Allow 3% |
| Alternative method 1: | ||
| \(\dfrac{65 \times 5}{100}\ (= 3.25)\) oe | M1 | |
| \(9.75 \div 3.25\) | M1 | FT ‘their 3.25’ |
| 3 ISW | A1 | Allow 3% |
| Alternative method 2: | ||
| \(9.75 \div 0.65\ (=15)\) oe | M1 | May be found using a build-up method |
| \(15 \div 5\) | M1 | FT ‘their 15’ |
| 3 ISW | A1 | Allow 3% |
| (6) | ||