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Date May 2017 Marks available 3 Reference code 17M.1.sl.TZ1.14
Level SL only Paper 1 Time zone TZ1
Command term Find 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.

[3]
a.

Find the value of \(n\).

[3]
b.

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]

a.

\(35\,300 = 9000{\left( {1 + \frac{{3.2}}{{100 \times 4}}} \right)^{4 \times n}}\)     (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]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 1 - Number and algebra » 1.9
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