Question 2 (Total marks for this question = 18 marks)
Continuous compounding is an important theoretical concept in Finance. Let i be the annual nominal
interest rate.
(a) State a formula for the future value FV of an investment with present value PV which is
compounded with compounding frequency m for n years. (1 mark)
(b) State a formula for the future value FV of an investment with present value PV which is
compounded with continuous compounding for n years. (1 mark)
(c) Show that the formula in (a) approaches the formula in (b) as the compounding frequency m
approaches infinity. (3 marks)
(d) State a formula for the effective annual interest rate of an investment which is compounded
with compounding frequency m. (1 mark)
(e) State a formula for the effective annual interest rate of an investment which is compounded
with continuous compounding. (1 mark)
(f) Show that the formula in (d) approaches the formula in (e) as the compounding frequency m
approaches infinity. (3 marks)
(g) For an investment of $1,000 with interest rate 10% per annum, calculate the future value FV
after one year with continuous compounding. (2 marks)
(h) Explain why the All Ordinaries Index is the broadest index on the Australian Securities
Exchange. (3 marks)
(i) Does the All Ordinaries Index compound continuously? Explain your answer. (3 marks)
Question 3 (Total marks for this question = 12 marks)
(a) What is the annual headline rate of inflation in Australia for the 2021-2022 financial year?
Give a reference in your references list at the end of your assignment. (2 marks)
(b) State the Fisher effect formula. (1 mark)
(c) Explain why the Fisher effect formula works. (3 marks)
(d) Approximate the Fisher effect formula if the rate of inflation is small. (3 marks)
(e) If a 12 month term deposit currently earns 2% per annum interest, what is the real rate of
return before tax? Use the annual headline rate of inflation from (a) when calculating the real
rate of return. (3 marks)