Foundation June 2024 Paper 3 Q17
17 Riley invests some money in a savings account that pays 4% simple interest per year.
After 5 years the total interest that Riley’s investment has earned is £360.
Find the total value of Riley’s investment after 5 years.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [£]2160 with correct working | 5 | Method 1 M3 for \(\dfrac{360}{5 \times 0.04}\) oe may be implied by 1800 or M2 for \(\dfrac{360}{0.04}\) oe or \(\dfrac{360}{5} \div 4\) or \(\dfrac{360}{4} \div 5\) or M1 for \(\dfrac{360}{5}\) or \(\dfrac{360}{4}\) or \(\dfrac{P \times 4 \times 5}{100} = 360\) oe AND M1dep for their \(1800 + 360\) | Correct working for 5 marks requires evidence of at least M2 N/C methods need labels or operators For M3: oe \(360 = 1800 \times 5 \times (0.04\) or \(4/100)\) or \(\dfrac{360}{20} \times 100\) or N/C e.g. 4% = 72, 1% = 18, 100% = 1800 or 20% = 360, 10% = 180, 100% = 1800 or 20% = 360, \(360 \times 5 = 1800\) or or 1 year = 90, 1% = 18, 100% = 1800 NB \(360 \times 5 = 1800\) alone scores M0 For M2: may be implied by 9000 or 18 or N/C e.g. 4% = 72, 1% = 18 or 20% = 360, 10% = 180 For M1: may be implied by 72 or 90 or N/C e.g. 4% = 72 or 20% = 360 “May be implied” tells you to look for the correct working associated with these values Their 1800 dependent on M3 and not spoiled |
| OR Method 2 Trials M2 for two complete trials bracketing 360 and resulting in 360 \(\pm 10\) or M1 for one complete trial \(\ne 360\) | Trials must show substitution and evaluation e.g. \(1850 \times 0.04 \times 5\) oe = 370 \(1750 \times 0.04 \times 5\) oe = 350 e.g. \(500 \times 0.04 \times 5\) oe = 100 | ||
| If 0 or 1 scored, instead award SC2 for 2160 If 0 scored, SC1 for £1661[.64] | with no working or insufficient working | ||
Appendix
Non Calculator methods for percentages.
Labels only
This is when labels such as 10% = are used. If only labels are used the final answer scores full marks if it is correct.
Condone a numerical slip if the answer is correct.
If there is an error in the values and so the final answer is incorrect this cannot score method marks
e.g. Find 65% of 80
| Method scoring M1A1 | 10% = 8 5% = 4 50% = 40 65% = 52 ✓ M1A1 | 10% = 8 5% = 5 ✖ condone this slip as answer correct 50% = 40 65% = 52 ✓ M1A1 |
| Method scoring M0A0 | 10% = 8 5% = 6 ✖ Do not condone this slip as answer incorrect 50% = 40 65% = 54 ✖ M0 |
Build up method
This is where the candidate finds the percentages to build up to the required value but shows the operations used.
e.g. Find 65% of 80
10% = \(80 \div 10 = x\)
5% = \(x \div 2 = y\)
50% = \(x \times 5 = z\)
65% = \(x + z + y\)
Because the operations have been shown and they are correct, if there is an error in one of \(x\), \(y\) or \(z\), method marks can still be earned
Examples of methods used for Q17 (There will be more)
When candidates say “4% =” they should mean “4% of the amount invested =” and not “4% of 360 =”
Make a professional judgement if this is correct.
\(360 \times 1.04\) or \(360 \times 0.04\) are good indicators of error.
4% of 360 = 14.40 and then \(14.40 \times 5 = 72\) is wrong method because they are finding 4% of the interest and not 4% of the original amount.
In the examples below, the M marks are earned by the statement with those preceding it. Not just for the statement.
In some methods, M2 evidence can never seen
| \(360 \div 5\) (= 72) M1 (72) \(\times\) 25 = (1800) M3 | or | 20% = 360 4% = 72 M1 100% = 1800 M3 |
| \(360 \div 5\) (= 72) M1 (72) \(\div\) 4 (= 18) M2 (18) \(\times\) 100 = (1800) M3 | or | 20% = 360 4% = 72 M1 1% = 18 M2 100% = 1800 M3 |
| \(360 \div 4\) (= 90) M1 (90) \(\div\) 5 (= 18) M2 (18) \(\times\) 100 = (1800) M3 | or | 20% = 360 1 year = 72 M1 1% = 18 M2 100% = 1800 M3 |
| \(360 \div 20\) (= 18) M2 (18) \(\times\) 100 = (1800) M3 | or | 20% = 360 1% = 18 M2 100% = 1800 M3 |
| \(360 \div 4\) (= 90) M1 (90) \(\div\) 5 (= 18) M2 (18) \(\times\) 100 = (1800) M3 | or | 20% = 360 5% = 90 M1 100% = 1800 M3 |
| \(360 \times 100\) = (36000) (36 000) \(\div\) 5 = 7200 M1 (7200) \(\div\) 4 = 1800 M3 | or | 20% = 360 5% = 90 M1 500% = 9000 100% = 1800 M3 |
Note: the scheme say “May be implied by 72” but, as shown in the example above, 72 can come from wrong method.
72 is a good guide to look for supporting evidence to judge if the figure comes from correct method.