Numeracy Higher November 2020 Unit 2 Q10
10. Dafydd has bought a new van.
To pay for the van, he has taken out a loan for £18 000.
The loan has an APR of 3%, and will be repaid by monthly payments of £237.84.
The amount that is still to be repaid on a loan is known as the remaining balance.
The formula below can be used to calculate the remaining balance on a loan after a period of time from the start date of the loan:
where,
\(r\) is the monthly interest rate written as a decimal,
\(L\) is the loan amount in pounds,
\(M\) is the monthly payment in pounds,
\(n\) is the number of months after the start date of the loan.
Dafydd plans to sell the van in 5 years’ time for £5000.
Will he have enough money from the sale of the van to pay off the remaining balance on the loan?
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Remaining balance =) \(18000(1+\ 0.0025)^{60}\ - 237.84\left(\frac{(1+\ 0.0025)^{60}-1}{0.0025}\right)\) | M2 | (= (£) 20 909.10(…) – (£) 15 375.57(…)) Each expression may be seen in stages M1 for a subtraction involving 1 correct expression, OR for a subtraction with only one consistently substituted incorrect value |
| = (£)5533.52(7…) AND e.g. ‘No, Dafydd would not have enough to pay off the loan’ | A2 | CAO Accept rounded answers e.g. (£)5533 or (£)5534 A1 for (£)5533.52(7…) or rounded answers without a correct conclusion, OR A1 for a correct calculation of (£)15 375.57(…) |