| Date | November 2017 | Marks available | 2 | Reference code | 17N.1.sl.TZ0.9 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Calculate | Question number | 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.
Calculate the difference between the original price of the bicycle and the total amount Juan will pay.
Markscheme
\(\frac{{560}}{{70}} \times 100\) (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.
OR
\({\text{N}} = \frac{1}{2}\)
\({\text{I% }} = 75\)
\({\text{PV}} = ( \pm )560\)
\({\text{P/Y}} = 1\)
\({\text{C/Y}} = 12\) (A1)(M1)
Note: Award (A1) for \({\text{C/Y}} = 12\) seen, (M1) for all other entries correct.
OR
\({\text{N}} = 6\)
\({\text{I% }} = 75\)
\({\text{PV}} = ( \pm )560\)
\({\text{P/Y}} = 12\)
\({\text{C/Y}} = 12\) (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]
