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STAT2032/6046 Assignment 1
Instructions to Students
1. This assignment has 1 question and is worth 10 marks.
2. This is an individual assignment worth 10% of your final grade.
3. You may submit your completed assignment in either a PDF document or an Excel
spreadsheet.
4. Regardless of the format of your submission, ensure you have shown sufficient
working and calculation in your solution. In particular, if you are answering the
assignment in a spreadsheet, ensure that formulas are entered for all calculations.
Hardcoded answers and intermediate answers will not earn any credit.
5. Complete and include the signed assignment cover sheet in your answer file. If you are
submitting an Excel spreadsheet, insert a new sheet and copy paste the completed cover
sheet as a screenshot/picture in this sheet.
6. Name your assignment with your student ID only – that is, ‘uXXXXXX’ (with the X’s
corresponding to your student ID exactly). Then submit your assignment (PDF / Excel)
via the designated link on the Wattle course page.
7. Assignment must be submitted by 9 pm on Friday 15 March. Late submission without
prior approval for extension will be given 0 mark.
Question 1 (10 marks)
Sam wants to deposit his savings of $10,000 in a low-risk investment account for 4 years. Sam
is considering investment in one of the three investment options with three different banks.
Option 1: Bank A offers a 4-year special variable interest savings account where an effective
simple interest rate of X per month is payable for the first 2 years and a compound nominal
interest rate of 5% per annum convertible monthly is payable in the last 2 years.
Option 2: Bank B offers a 1-year term deposit at a nominal interest rate of 6% per annum
convertible 0.2 times a year. After one year, Sam would have to roll over the investment into a
new 3-year term deposit at bank B. While the crediting rate for the future 3-year term deposit
is currently unknown, Sam expects it to be around a nominal rate of discount of Y per annum
convertible 0.2 times a year. This expectation is based on rumours Sam heard from his friends.
Therefore, Sam is not very confident in his expectation.
Option 3: Bank C offers a savings account that pays an indexed floating interest rate
continuously. Sam believes the indexed floating annual force of interest over the coming 4
years follows the formula below. Moreover, based on the formula below, the present value at
the end of 1 year of $1 payable at the end of 3 years is 15% larger than the present value at
time 0 of $1 payable at the end of 4 years.
!(#) = &0.068+!"."$% 0 ≤ # ≤ 3 0.068+!"."& + 0(# − 3) 3 < # ≤ 4
a) After performing some calculations, Sam realises that all three banks would provide the
same accumulated value at the end of four years. Find the value of X, Y and Z, rounded to
5 decimal places. [7 marks]
b) While Sam is confident about his estimation of the parameters 0.068 and Z for his
projection on the indexed floating rate, Sam is somewhat uncertain about the parameter
0.01 although he is sure that the actual parameter value should be within the range of
(0,0.01] (i.e. larger than 0 but no larger than 0.01). Considering all the information given,
explain which investment option Sam is likely to choose. [3 marks]