Numeracy Higher November 2021 Unit 2 Q8
8. Melissa wants to buy a new car. The car she’d like to buy is priced at £17 000.
Melissa needs to take out a loan to buy the car.
Melissa is considering taking out a loan of £17 000 from her bank.
The bank will charge her interest on the loan, at a rate of 0·25% per month.
Melissa wants to calculate the monthly payments required to pay off the loan.
The formula she will use is:
where,
\(r\) is the monthly interest rate written as a decimal,
\(L\) is the loan amount, and
\(n\) is the number of months required to pay off the loan.
Calculate the difference in the monthly payments if the loan is taken out over 4 years rather than 5 years. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Difference in monthly payments =) \(\dfrac{0.0025 \times 17000}{1 - (1 + 0.0025)^{-48}}\) or \(\dfrac{0.0025 \times 17000}{1 - (1 + 0.0025)^{-60}}\) | M1 | Each expression may be seen in stages |
| = (£)376.28(…) or (£)305.46(7…) | A1 | |
| \(\dfrac{0.0025 \times 17000}{1 - (1 + 0.0025)^{-48}} - \dfrac{0.0025 \times 17000}{1 - (1 + 0.0025)^{-60}}\) | M1 | |
| = (£)70.81 | A1 | Accept (£)70.82 or (£)70.815(8…) if accurate monthly payments used If no marks awarded, SC1 for a final answer of (£)0.08 or (£)0.09 or (£)0.088(2…) from using 0.25 instead of 0.0025 OR SC1 for a final answer of (£)62.09 or (£)62.094(…) from using 0.025 instead of 0.0025 OR SC1 for a final answer of (£)851.05 or (£)851.06 or (£)851.053(…) from using the correct rate with n = 4 and n = 5 |