Foundation June 2019 Paper 3 Q26
26 Mia wants to borrow £6000 and repay it, with interest, after two years.
She sees two offers for loans.
| Offer 1 Compound interest 3% per year | Offer 2 Compound interest First year 1% Second year 5% |
Mia says,
“I will pay back the same amount because the average of 1% and 5% is 3%”
Is she correct?
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(6000 \times 1.03\) or 6180 or \(6000 \times 0.03\) or 180 or \(6000 \times 1.01\) or 6060 or \(6000 \times 0.01\) or 60 | M1 | \(6000 \times 1.05\) or 6300 \(6000 \times 0.05\) or 300 |
| their \(6180 \times 1.03\) or 6365.4(0) or their \(6180 \times 0.03\) or 185.4(0) or 365.4(0) or their \(6060 \times 1.05\) or 6363 or their \(6060 \times 0.05\) or 303 or 363 | M1dep | \(6000 \times 1.03^2\) or \(6000 \times 1.0609\) or \(6000 \times 1.01 \times 1.05\) or \(6000 \times 1.0605\) or \(6300 \times 1.01\) or \(6300 \times 0.01\) or 63 |
| 6365.4(0) and 6363 and No or 365.4(0) and 363 and No | A1 | accept 2.4(0) difference to imply ‘No’ |
| Alternative method 2 | ||
| 1.03 or 1.01 or 1.05 | M1 | |
| \(1.03^2\) or \(1.03 \times 1.03\) or 1.0609 or 0.0609 or 6.09(%) or \(1.01 \times 1.05\) or 1.0605 or 0.0605 or 6.05(%) | M1dep | |
| 1.0609 and 1.0605 and No or 0.0609 and 0.0605 and No or 6.09(%) and 6.05(%) and No | A1 | accept 0.0004 difference to imply ‘No’ accept 0.04(%) difference to imply ‘No’ |
Additional guidance
| Accept any clear indication that the Offer 1 amount is different to the Offer 2 amount for ‘No’ | |
| If build up methods are used they must be complete | |
| \(6000 \times 0.03^2\) implies \(6000 \times 0.03\) | M1 |
| \(1.03^3\) implies 1.03 | M1 |
| 360 without 180 seen (simple interest) | M0 |
| If a different starting value is used, apply Alt 2 with correctly evaluated answers eg \(600 \times 1.03^2 = 636.54\) \(600 \times 1.01 \times 1.05 = 636.30\) No, pay less with Offer 1 (condone incorrect choice of Offer 1) \(500 \times 1.03 = 515 \quad 515 \times 1.03 = 530.45\) \(500 \times 1.01 = 505 \quad 505 \times 1.05 = 530.25\) No, they are different | M1M1A1 M1M1A1 |