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)

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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 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)