Question 1
Consider an investment of $1,000.
(a) Using a financial calculator, calculate the time taken for this investment to double in value to $2,000 at an interest rate of 2% per annum compounded annually. Round your answer to the nearest year.
(b) Using a financial calculator, calculate the time taken for this investment to double in value to $2,000 at an interest rate of 5% per annum compounded annually. Round your answer to the nearest year.
(c) Using a financial calculator, calculate the time taken for this investment to double in value to $2,000 at an interest rate of 7% per annum compounded annually. Round your answer to the nearest year.
(d) Using your answers to (a), (b) and (c), write down a simple mathematical formula for doubling time D 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 quadrupling time Q years in terms of the annual interest rate i % with annual compounding. Your formula should be valid for low interest rates.
(f) Using your answer to (e), calculate the time taken for an investment to quadruple in value for i=2, i=5 and i=7.
Question 2
(a) Find and show the individual income tax rates in Australia for Australian Residents for the 2014-2015 financial year. Give a reference in your references list at the end of your assignment.
(b) Using your answer to (a), calculate the income tax payable by an individual with a taxable income in the 2014-2015 financial year of : (i) $19,000 (ii) $37,000 (iii) $60,000 (iv) $100,000 (v) $190,000.
Question 3
Suppose $1,000 is invested for 1 year at an interest rate of 4.5% per annum compounded. Assume there are 365 days in 1 year.
(a) Using a financial calculator, calculate the future value (FV) to the nearest cent (that is, to 2 decimal places) if the compounding is performed : (i) annually (ii) 6 monthly (iii) quarterly (iv) monthly (v) daily (vi) hourly
(b) Calculate the future value (FV) to the nearest cent with continuous compounding. Explain why the answer is the same as in (a)(vi).
(c) Using a financial calculator, calculate the effective annual interest rate as a percentage to 4 decimal places if the compounding is performed : (i) annually (ii) 6 monthly (iii) quarterly (iv) monthly (v) daily (vi) hourly
(d) Calculate the effective annual interest rate to 4 decimal places with continuous compounding. Explain why the answer is the same as in (c)(vi).
Question 4
Consider a machine which an Australian company bought for $50,000 five years ago. The machine has an expected life of 10 years and an expected salvage value of zero. The company uses straight-line depreciation.
(a) Calculate the amount of annual depreciation.
(b) Calculate the current book value of the machine.
(c) State the current company tax rate in Australia.
(d) If the machine were sold today for $10,000, what would be the taxes associated with the sale?
(e) If the machine were sold today for $25,000, what would be the taxes associated with the sale?
(f) If the machine were sold today for $40,000, what would be the taxes associated with the sale?
Question 5
Write a short essay discussing the origins of the Global Financial Crisis (GFC) and also draw a table showing Australia's official interest rate known as the cash rate from August, 2007, to August, 2014. Explain why the cash rate has been held at a record low of 2.5% per annum for the most recent one year period. Remember to give references in your references list at the end of your assignment.