Question 1 (Total marks for this question 15 marks) Consider an investment of $1,000 (a) Calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 2 per annum compounded annually Round your answer down to the nearest year (2 marks) (b) Calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 5 per annum compounded annually Round your answer down to the nearest year (2 marks) (c) Calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 10 per annum compounded annually Round your answer down to the nearest year (2 marks) (d) Using your answers to (a), (b) and (c), write down a simple mathematical formula for trebling time T years in terms of the annual interest rate i with annual compounding Do not use the logarithmic (log) function in your formula Your formula should be valid for low interest rates Illustrate that your formula works for i 2, i 5 and i 10 (6 marks) (e) Some analysts predict that property prices in some parts of Australia treble approximately every 15 years Using your answer to (d), what would be the approximate annual rate of return for property investors in this situation (3 marks) 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) Question 4 (Total marks for this question 15 marks) The rate of return for bonds issued by the Australian Commonwealth Government Treasury is given as 4 per annum The expected return for the Australian share market is given as 12 per annum An investor wishes to analyse the expected rate of return for some listed companies The rate of inflation is given as 2 per annum (a) Calculate the market risk premium (1 mark) (b) Calculate an investors expected rate of return for a companys shares if the company has beta value of 1 (2 marks) (c) Calculate an investors expected rate of return for a companys shares if the company has beta value of 0 5 Explain why the answer is less than the answer in (b) (3 marks) (d) Calculate an investors expected rate of return for a companys shares if the company has beta value of 2 Explain why the answer is more than the answer in (b) (3 marks) (e) Determine the expected real rate of return in (b) (3 marks) (f) Explain why Australian Commonwealth Government Treasury Bonds are risk free (3 marks)

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Question 1 (Total marks for this question = 15 marks) Consider an investment of $1,000. (a) Calculate the time taken for this investment to treble

Question 1 (Total marks for this question = 15 marks)

Consider an investment of $1,000.

(a) Calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 2% per annum compounded annually. Round your answer down to the nearest year. (2 marks)
(b) Calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 5% per annum compounded annually. Round your answer down to the nearest year. (2 marks)
(c) Calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 10% per annum compounded annually. Round your answer down to the nearest year. (2 marks)
(d) Using your answers to (a), (b) and (c), write down a simple mathematical formula for trebling time T years in terms of the annual interest rate i % with annual compounding. Do not use the logarithmic (log) function in your formula. Your formula should be valid for low interest rates. Illustrate that your formula works for i=2, i=5 and i=10. (6 marks)
(e) Some analysts predict that property prices in some parts of Australia treble approximately every 15 years. Using your answer to (d), what would be the approximate annual rate of return for property investors in this situation? (3 marks)

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)

Question 4 (Total marks for this question = 15 marks)

The rate of return for bonds issued by the Australian Commonwealth Government Treasury is given as 4% per annum. The expected return for the Australian share market is given as 12% per annum. An investor wishes to analyse the expected rate of return for some listed companies. The rate of inflation is given as 2% per annum.

(a) Calculate the market risk premium. (1 mark)
(b) Calculate an investors expected rate of return for a companys shares if the company has beta

value of 1. (2 marks)
(c) Calculate an investors expected rate of return for a companys shares if the company has beta

value of 0.5. Explain why the answer is less than the answer in (b). (3 marks)
(d) Calculate an investors expected rate of return for a companys shares if the company has beta

value of 2. Explain why the answer is more than the answer in (b). (3 marks)
(e) Determine the expected real rate of return in (b). (3 marks)
(f) Explain why Australian Commonwealth Government Treasury Bonds are risk-free.

(3 marks)