| Date | May 2017 | Marks available | 3 | Reference code | 17M.1.sl.TZ1.14 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Give your answer and Calculate | Question number | 14 | Adapted from | N/A |
Question
Arthur and Jacob dream of owning a speedboat that costs \({\text{35}}\,{\text{300}}\) euros (EUR).
Arthur invested \(x\) EUR in an account that pays a nominal annual interest rate of 3.6%, compounded monthly. After 18 years he will have \({\text{35}}\,{\text{300}}\) EUR in the account.
Jacob invested 9000 EUR for \(n\) years. The investment has a nominal annual interest rate of 3.2% and is compounded quarterly. After \(n\) years, the investment will be worth \({\text{35}}\,{\text{300}}\) EUR.
Calculate the value of Arthur’s initial investment, \(x\). Give your answer to two decimal places.
Find the value of \(n\).
Markscheme
\(35\,300 = PV{\left( {1 + \frac{{3.6}}{{100 \times 12}}} \right)^{12 \times 18}}\) (M1)(A1)
Note: Accept “\(x\)” instead of \(PV\). Award (M1) for substitution into compound interest formula, (A1) for correct substitution.
OR
\(N = 18\)
\(I\% = 3.6\)
\(FV = ( \pm )35\,300\)
\(P/Y = 1\)
\(C/Y = 12\) (A1)(M1)
Note: Award (A1) for \(C/Y = 12\) seen, (M1) for all other correct entries.
OR
\(N = 216\)
\(I\% = 3.6\)
\(FV = ( \pm )35\,300\)
\(P/Y = 12\)
\(C/Y = 12\) (A1)(M1)
Note: Award (A1) for \(C/Y = 12\) seen, (M1) for all other correct entries.
\(PV = 18483.03\) (A1) (C3)
[3 marks]
\(35\,300 = 9000{\left( {1 + \frac{{3.2}}{{100 \times 4}}} \right)^{4 \times n}}\) (M1)(A1)
Note: Award (M1) for substitution into compound interest formula and equating to \(35\,300\), (A1) for correct substitution.
OR
\(I\% = 3.2\)
\(PV = ( \pm )9000\)
\(FV = ( \mp )35\,300\)
\(P/Y = 1\)
\(C/Y = 4\) (A1)(M1)
Note: Award (A1) for \(C/Y = 4\) seen, (M1) for all other correct entries.
OR
\(I\% = 3.2\)
\(PV = ( \pm )9000\)
\(FV = ( \mp )35\,300\)
\(P/Y = 4\)
\(C/Y = 4\) (A1)(M1)
Note: Award (A1) for \(C/Y = 4\) seen, (M1) for all other correct entries.
\(n = 43\) (A1) (C3)
[3 marks]
