Numeracy Higher November 2019 Unit 2 Q12
12. Laura and Matthew are buying a house priced at £150 000.
In order to buy the house, they will need to have a mortgage.
A mortgage is a loan that is paid back over a number of years.
They have saved a deposit of £15 000.
They need a mortgage of £135 000.
A bank has offered them a mortgage of £135 000 at an interest rate of 2·4% per annum, with interest added monthly.
To calculate the monthly payments needed in order to pay back the mortgage, they use the following formula:
\[M = \frac{r \times P}{1-(1+r)^{-12n}}\]where:
\(M\) is the amount of each monthly payment,
\(P\) is the mortgage needed,
\(r\) is the monthly interest rate as a decimal,
\(n\) is the number of years taken to pay back the mortgage.
What is the monthly rate, as a decimal?
Circle your answer. [1]
0·24 0·024 0·00002 0·002 0·2
They have correctly calculated their monthly payments to be £598.86 when paying back the mortgage over 25 years.
How much more will it cost in total to pay back the mortgage over 30 years than over 25 years? [5]
| Scheme | Marks | Comments |
|---|---|---|
| 0.002 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| (M =) \(\dfrac{0.002 \times 135\,000}{1-(1+0.002)^{-12 \times 30}}\) | M2 | FT from (a) M1 for one error in substitution OR for 1 slip in the formula, but ‘their 0.002’ must be correctly substituted The use of 25 instead of 30 is M0 as this is a check for the monthly payments for 25 years |
| = (£) 526.42(08…) | A1 | ISW FT from M2 only Rate of 0.24 leads to (£) 32 400 Rate of 0.024 leads to (£) 3240.63(4…) Rate of 0.00002 leads to (£) 376.35(5…) Rate of 0.2 leads to (£) 27 000 |
| 526.42 × 360 – 598.86 × 300 | M1 | (£)189511.2(0) – (£)179658 FT ‘their (£)526.42’ |
| = (£) 9853.2(0) | A1 | Only FT provided their answer > 0 Allow the following Use of unrounded 526.42(0..) leads to (£)9853.50(4..) Use of unrounded 526.42(0…) AND 598.85(6…) leads to (£)9854.61(5…) |