Higher November 2018 Paper 2 Q11
11. Ms Leighton arranged a £15 000 loan for 22 years to buy a canal boat.
After 22 years the loan is to be paid back in full together with compound interest at 3·4% per annum.
(a) Ms Leighton did not plan to make any payments during the 22 years.
How much would Ms Leighton need to pay back after 22 years? [3]
How much would Ms Leighton need to pay back after 22 years? [3]
(b) In fact, Ms Leighton paid off £10 000 of the loan in a single payment at the end of 10 years.
For each of the next 12 years compound interest continues to be charged at rate of 3·4% per annum on the amount owed.
How much would Ms Leighton pay back in total during the full period of the loan?
Give your answer to the nearest £. [4]
For each of the next 12 years compound interest continues to be charged at rate of 3·4% per annum on the amount owed.
How much would Ms Leighton pay back in total during the full period of the loan?
Give your answer to the nearest £. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \(15000 \times 1.034^{22}\) | M2 | M1 for indication of \(15000 \times 1.034\) (= 15510) or equivalent |
| (= £) 31299(.91...) | A1 | Accept (£)31300 |
| Scheme | Marks | Comments |
|---|---|---|
| \(15000 \times 1.034^{10}\) ( = £ 20955.433...) | M1 | |
| \(15000 \times 1.034^{10} - 10000\) ( = £ 10955.43...) | m1 | |
| \(10955(.43\ldots) \times 1.034^{12}\) (= £16363.49...) | M1 | FT ‘their derived £10955.43...’ FT from ‘£10955’ gives (£)16362.846... |
| (Total pay back 10000 + 16363 =) (£) 26363 | A1 | CAO, accept an answer that rounds to (£) 26363 |
| (7) |