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Date	November 2017	Marks available	4	Reference code	17N.1.SL.TZ0.T_9
Level	Standard Level	Paper	Paper 1 (with calculator from previous syllabus)	Time zone	Time zone 0
Command term	Calculate	Question number	T_9	Adapted from	N/A

Question

Juan buys a bicycle in a sale. He gets a discount of 30% off the original price and pays 560 US dollars (USD).

To buy the bicycle, Juan takes a loan of 560 USD for 6 months at a nominal annual interest rate of 75%, compounded monthly. Juan believes that the total amount he will pay will be less than the original price of the bicycle.

Calculate the original price of the bicycle.

[2]

Calculate the difference between the original price of the bicycle and the total amount Juan will pay.

[4]

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$\frac{{560}}{{70}} \times 100$ (or equivalent) (M1)

Note: Award (M1) for dividing 560 by 0.7 or equivalent.

$= 800{\text{ (USD)}}$ (A1) (C2)

[2 marks]

$560{\left( {1 + \frac{{75}}{{12 \times 100}}} \right)^{12 \times \frac{1}{2}}}$ (M1)(A1)

Note: Award (M1) for substitution into interest formula, (A1) for their correct substitution.

${\text{N}} = \frac{1}{2}$

${\text{I% }} = 75$

${\text{PV}} = ( \pm )560$

${\text{P/Y}} = 1$

${\text{C/Y}} = 12$ (A1)(M1)

Note: Award (A1) for ${\text{C/Y}} = 12$ seen, (M1) for all other entries correct.

${\text{N}} = 6$

${\text{I% }} = 75$

${\text{PV}} = ( \pm )560$

${\text{P/Y}} = 12$

${\text{C/Y}} = 12$ (A1)(M1)

Note: Award (A1) for ${\text{C/Y}} = 12$ seen, (M1) for all other entries correct.

$= 805.678 \ldots {\text{ (USD)}}$ (A1)

Note: Award (A3) for 805.678… (806) seen without working.

(Juan spends) 5.68 (USD) (5.67828… USD) (more than the original price) (A1)(ft) (C4)

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » SL 1.4—Financial apps – compound int, annual depreciation

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