Date | May 2011 | Marks available | 3 | Reference code | 11M.2.sl.TZ2.2 |
Level | SL only | Paper | 2 | Time zone | TZ2 |
Command term | Calculate | Question number | 2 | Adapted from | N/A |
Question
Give all your numerical answers correct to two decimal places.
On 1 January 2005, Daniel invested 30000 AUD at an annual simple interest rate in a Regular Saver account. On 1 January 2007, Daniel had 31650 AUD in the account.
On 1 January 2005, Rebecca invested 30000 AUD in a Supersaver account at a nominal annual rate of 2.5% compounded annually. Calculate the amount in the Supersaver account after two years.
On 1 January 2005, Rebecca invested 30000 AUD in a Supersaver account at a nominal annual rate of 2.5% compounded annually.
Find the number of complete years since 1 January 2005 it would take for the amount in Rebecca’s account to exceed the amount in Daniel’s account.
On 1 January 2007, Daniel reinvested 80% of the money from the Regular Saver account in an Extra Saver account at a nominal annual rate of 3% compounded quarterly.
(i) Calculate the amount of money reinvested by Daniel on the 1 January 2007.
(ii) Find the number of complete years it will take for the amount in Daniel’s Extra Saver account to exceed 30000 AUD.
Markscheme
Amount=30000(1+2.5100)2 (M1)(A1)
Note: Award (M1) for substitution into compound interest formula, (A1) for correct substitution.
31518.75 AUD (A1)(G2)
OR
I=30000(1+2.5100)2−30000 (M1)(A1)
Note: Award (M1) for substitution into compound interest formula, (A1) for correct substitution.
31518.75 AUD (A1)(G2)
[3 marks]
Rebecca's amount=30000(1+2.5100)n
Daniel's amount=30000+30000×2.75×n100 (M1)(A1)(ft)
Note: Award (M1) for substitution in the correct formula for the two amounts, (A1) for correct substitution. Follow through from their expressions used in part (a) and/or part (b).
OR
2 lists of values seen (at least 2 terms per list) (M1)
lists of values including at least the terms with n=8 and n=9 (A1)(ft)
For n=8 CI=36552.09 SI=36600
For n=9 CI=37465.89 SI=37425
Note: Follow through from their expressions used in part (a) or/and (b).
OR
Sketch showing 2 graphs, one exponential and the other straight line (M1)
point of intersection identified (M1)
Note: Follow through from their expressions used in part (a) or/and (b).
n=9 (A1)(ft)(G2)
Note: Answer 8.57 without working is awarded (G1).
Note: Accept comparison of interests instead of the total amounts in the two accounts.
[3 marks]
(i) 0.80×31650=25320 (M1)(A1)(G2)
Note: Award (M1) for correct use of percentages.
(ii) 25320(1+34×100)4n>30000 (M1)(M1)(ft)
Notes: Award (M1) for correct left-hand side of the inequality, (M1) for comparison to 30000. Accept equation. Follow through from their answer to part (d) (i).
OR
List of values from their 25320(1+34×100)4n seen (at least 2 terms) (M1)
Their correct values for n=5 (29401.18) and n=6 (30293) seen (A1)(ft)
Note: Follow through from their answer to (d) (i).
OR
Sketch showing 2 graphs – an exponential and a horizontal line (M1)
Point of intersection identified or vertical line drawn (M1)
Note: Follow through from their answer to (d) (i).
n=6 (A1)(ft)(G2)
Note: Award (G1) for answer 5.67 with no working.
[5 marks]
Examiners report
Part b) was well done.
Parts c) and d) were not answered well. Marks were gained by candidates who showed detailed working. Many candidates had difficulty working with the compound interest formula where the interest was compounded quarterly. Correct final answers in parts c) and d) were rare.
Parts c) and d) were not answered well. Marks were gained by candidates who showed detailed working. Many candidates had difficulty working with the compound interest formula where the interest was compounded quarterly. Correct final answers in parts c) and d) were rare.