Consider an investor who has $1,000,000 to invest and is looking to buy an investment property in a large city in Australia. The investor has been told by a property analyst that property in this city is a good investment because property prices there have approximately doubled every 10 years. The investor is also considering investing in a term deposit at a major bank in Australia with an interest rate offered of 3% per annum compounded annually. The investor wants to determine whether to invest in a term deposit or to buy an investment property.

(a) Calculate the time taken for an investment of $1,000,000 to double in value to $2,000,000 at

an interest rate of : (i) 2% per annum compounded annually (ii) 3% per annum compounded

annually (iii) 4% per annum compounded annually. Round your answers up to the nearest

year. What do you observe when each of your answers is multiplied by the respective interest

rate? (7 marks)

(b) Write down the Rule of 72 for doubling time D years in terms of the annual interest rate i %

with annual compounding. The formula for the Rule of 72 is valid for low interest rates. By

comparing your answers to (a), illustrate that your formula works. (2 marks)

(c) Assuming that property prices in this city double approximately every 10 years, using the

Rule of 72, what would be the approximate annual rate of return for property investors in this

situation? (2 marks)

(d) Using your answer to (c) and ignoring the effect of any taxes, explain whether the investor

should invest in a term deposit or buy an investment property. (2 marks)

(e) Write down the Rule of 70 for doubling time D years in terms of the annual interest rate i %

with annual compounding. Compare and contrast with the Rule of 72. (4 marks)