Consider an investment of $1,000. Using a financial calculator, calculate the ti

Question

Consider an investment of $1,000.

Using a financial calculator, 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)

Using a financial calculator, 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)

Using a financial calculator, 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)

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)

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?(2 marks)

Explanation / Answer

1. Principal = $1,000. Amount = $3,000. r = 2%.

Using the compounding formula: A = P(1+r/100)^n; 3,000 = 1,000*(1.02)^n

3 = 1.02^n or n = 55.478 years or 55 years (rounded off to nearest) (1.02^55.478 = 3).

2.

Principal = $1,000. Amount = $3,000. r = 5%.

Using the compounding formula: A = P(1+r/100)^n; 3,000 = 1,000*(1.05)^n

3 = 1.05^n or n = 22.5 years or 23 years (rounded off to the nearest year)

3.

Principal = $1,000. Amount = $3,000. r = 10%.

Using the compounding formula: A = P(1+r/100)^n; 3,000 = 1,000*(1.10)^n

3 = 1.10^n or n = 11.5 years or 12 years (rounded off to the nearest year)

4. when i = 2%, n = 55 years. when i = 5%, n = 23 years and when i = 10%, n = 12 years.

so, the approximate formula = (110/i)+1

when i = 2, n = 110/2 + 1 = 55+1 = 56. when i = 5, n = 110/5 + 1 = 23. when i = 10, n = 110/10 + 1 = 12.

5. Now n = (110/i)+1

or 15 = (110/i)+1

or 14 = 110/i

or i = 110/14 = 7.86%

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