Consider an investment of $1,000.
(a) Calculate the time taken for this investment to quadruple in value to $4,000 at an interest rate of 2% per annum compounded annually. Round your answer down to the nearest year.
(b) Calculate the time taken for this investment to quadruple in value to $4,000 at an interest rate of 5% per annum compounded annually. Round your answer down to the nearest year.
(c) Calculate the time taken for this investment to quadruple in value to $4,000 at an interest rate of 7% per annum compounded annually. Round your answer down to the nearest year.
(d) Using your answers to (a), (b) and (c), write down a simple mathematical formula for quadrupling time Q 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=7.
(e) Using your answer to (d), write down a simple mathematical formula for doubling time D years in terms of the annual interest rate i % with annual compounding. Your formula should be valid for low interest rates.