| Date | November 2010 | Marks available | 3 | Reference code | 10N.2.sl.TZ0.4 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Show that | Question number | 4 | Adapted from | N/A |
Question
Give all answers in this question correct to two decimal places.
Part A
Estela lives in Brazil and wishes to exchange 4000 BRL (Brazil reals) for GBP (British pounds). The exchange rate is 1.00 BRL = 0.3071 GBP. The bank charges 3 % commission on the amount in BRL.
Give all answers in this question correct to two decimal places.
Part B
Daniel invests $1000 in an account that offers a nominal annual interest rate of 3.5 % compounded half yearly.
Find, in BRL, the amount of money Estela has after commission.
Find, in GBP, the amount of money Estela receives.
After her trip to the United Kingdom Estela has 400 GBP left. At the airport she changes this money back into BRL. The exchange rate is now 1.00 BRL = 0.3125 GBP.
Find, in BRL, the amount of money that Estela should receive.
Estela actually receives 1216.80 BRL after commission.
Find, in BRL, the commission charged to Estela.
The commission rate is t % . Find the value of t.
Show that after three years Daniel will have $1109.70 in his account, correct to two decimal places.
Write down the interest Daniel receives after three years.
Markscheme
4000 × 0.97 = 3880.00 (3880) (M1)(A1)(G2)
Note: Award (M1) for multiplication of correct numbers.
OR
3 % of 4000 = 120 (A1)
4000 – 120 = 3880.00 (3880) (A1)(G2)
[2 marks]
3880 × 0.3071 = 1191.55 (M1)(A1)(ft)(G2)
Note: Award (M1) for multiplication of correct numbers. Follow through from their answer to part (a).
[2 marks]
\(\frac{{400}}{{0.3125}}\) (M1)
= 1280.00 (1280) (A1)(G2)
Note: Award (M1) for division of correct numbers.
[2 marks]
63.20 (A1)(ft)
Note: Follow through (their (c) –1216.80).
[1 mark]
\(t = \frac{{63.20 \times 100}}{{1280}}\) (M1)
t = 4.94 (A1)(ft)(G2)
Note: Follow through from their answers to parts (c) and (d).
[2 marks]
\({\text{A}} = 1000{\left( {1 + \frac{{3.5}}{{2 \times 100}}} \right)^6} = 1109.7023...\) (M1)(A1)(A1)
= 1109.70 (AG)
Notes: Award (M1) for substitution into correct formula, (A1) for correct substitution, (A1) for unrounded answer. If 1109.70 not seen award at most (M1)(A1)(A0).
OR
\({\text{I}} = 1000{\left( {1 + \frac{{3.5}}{{2 \times 100}}} \right)^6} - 1000 = 109.7023\) (M1)(A1)
A = 1109.7023... (A1)
= 1109.70 (AG)
Note: Award (M1) for substitution into correct formula, (A1) for correct substitution, (A1) for unrounded answer.
[3 marks]
109.70 (A1)
Note: No follow through here.
[1 mark]
Examiners report
Most of the students were penalized in this question for not given their money answers correct to the specified accuracy (2 decimal places).
The first three parts were well done. Some students gave their answer to part (d) in (e) and their answer to (e) in (d). This means that when reading commission they directed their answers to a percentage (commission rate).
Most of the students were penalized in this question for not given their money answers correct to the specified accuracy (2 decimal places).
The first three parts were well done. Some students gave their answer to part (d) in (e) and their answer to (e) in (d). This means that when reading commission they directed their answers to a percentage (commission rate).
Most of the students were penalized in this question for not given their money answers correct to the specified accuracy (2 decimal places).
The first three parts were well done. Some students gave their answer to part (d) in (e) and their answer to (e) in (d). This means that when reading commission they directed their answers to a percentage (commission rate).
Most of the students were penalized in this question for not given their money answers correct to the specified accuracy (2 decimal places).
The first three parts were well done. Some students gave their answer to part (d) in (e) and their answer to (e) in (d). This means that when reading commission they directed their answers to a percentage (commission rate).
Most of the students were penalized in this question for not given their money answers correct to the specified accuracy (2 decimal places).
The first three parts were well done. Some students gave their answer to part (d) in (e) and their answer to (e) in (d). This means that when reading commission they directed their answers to a percentage (commission rate).
Most of the students were penalized in this question for not given their money answers correct to the specified accuracy (2 decimal places).
Most of the students used the correct formula but not all made the correct substitution. From those that made the correct substitution, very few showed the unrounded answer. Part (b) was well done. In part (c) the majority did not put the interest (only) in the formula but the total amount $1109.70.
Most of the students were penalized in this question for not given their money answers correct to the specified accuracy (2 decimal places).
Most of the students used the correct formula but not all made the correct substitution. From those that made the correct substitution, very few showed the unrounded answer. Part (b) was well done. In part (c) the majority did not put the interest (only) in the formula but the total amount $1109.70.
