Numeracy Higher November 2023 Unit 2 Q7
7. Carys is buying a new caravan, priced at £20 000.
She is going to take out a loan to buy the caravan.
The table below shows her finance options.
The monthly payment is missing from Option B.
| Option A | Option B | |
|---|---|---|
| Deposit | £0 | £2000 |
| Loan amount | £20 000 | £18 000 |
| Loan period | 5 years | 4 years |
| APR of the loan | 3·3% | 3·3% |
| Monthly payment | £362.05 |
The formula for calculating the monthly payment on a loan is
\[M = \frac{r \times L}{1 - (1 + r)^{-n}}\]where:
- \(M\) is the amount of each monthly payment
- \(L\) is the loan needed
- \(r\) is the monthly interest rate as a decimal
- \(n\) is the number of months taken to pay back the loan.
(a)
Show that Carys’s monthly payment for Option B would be £400.81, correct to the nearest penny. [3]
(b)
Carys chooses Option B, rather than Option A.
Calculate how much Carys would save on the total amount paid for the caravan. [3]
Carys would save £ ……………
| Scheme | Marks | Comments |
|---|---|---|
| (Monthly payments =) | The correct answer alone, without any workings is awarded M0A0, since it is given in the question | |
| \(\dfrac{\frac{0.033}{12} \times 18000}{1 - \left(1 + \frac{0.033}{12}\right)^{-4 \times 12}}\) OR \(\dfrac{0.00275 \times 18000}{1 - (1 + 0.00275)^{-48}}\) or equivalent | M2 | M1 for an expression with only 1 (possibly repeated) incorrect substitution, but do not allow use of r = 3.3 |
| = (£)400.81 | A1 | Accept (£)400.80(89843…) Convincing working must be seen |
| Scheme | Marks | Comments |
|---|---|---|
| (Saving =) 362.05×5×12 − 400.81×4×12 (− 2000) or 362.05×60 − 400.81×48 (− 2000) | M1 | Use of accurate values of (£)362.05 and/or (£)400.81 can be accepted |
| = (£)484.12 | A2 | FT if more accurate values used e.g.
|
Corrected by Westie's Workshop
- The board's mark scheme printed “(£)484.94(84006)” and “(£)2484.94(84006)”. Changed to “(£)483.94(84006)” and “(£)2483.94(84006)” because using both accurate monthly payments gives a saving of £483.9484006… (or £2483.9484006… if the £2000 deposit is not taken off), as the rounded values £483.95 and £2483.95 next to them show.
Original: see the board's mark scheme PDF (link above).