Date | November 2016 | Marks available | 1 | Reference code | 16N.2.AHL.TZ0.H_12 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Write down | Question number | H_12 | Adapted from | N/A |
Question
On the day of her birth, 1st January 1998, Mary’s grandparents invested in a savings account. They continued to deposit on the first day of each month thereafter.
The account paid a fixed rate of 0.4% interest per month. The interest was calculated on the last day of each month and added to the account.
Let be the amount in Mary’s account on the last day of the month, immediately after the interest had been added.
Find an expression for and show that .
(i) Write down a similar expression for and .
(ii) Hence show that the amount in Mary’s account the day before she turned 10 years old is given by .
Write down an expression for in terms of on the day before Mary turned 18 years old showing clearly the value of .
Mary’s grandparents wished for the amount in her account to be at least the day before she was 18. Determine the minimum value of the monthly deposit required to achieve this. Give your answer correct to the nearest dollar.
As soon as Mary was 18 she decided to invest of this money in an account of the same type earning 0.4% interest per month. She withdraws every year on her birthday to buy herself a present. Determine how long it will take until there is no money in the account.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
A1
A1
AG
Note: Accept an argument in words for example, first deposit has been in for two months and second deposit has been in for one month.
[2 marks]
(i) (M1)A1
A1
(ii) (A1)
M1A1
AG
[6 marks]
A1
[1 mark]
(A1)(M1)(A1)
Note: Award (A1) for , (M1) for attempting to solve and (A1) for .
A1
Note: Accept . Accept .
[4 marks]
(M1)
(A1)(M1)(A1)
Note: Award (A1) for the equation (with their value of ), (M1) for attempting to solve for and (A1) for
A1
Note: Accept .
[5 marks]