Please do the full calculation through the financial calculator formula as per the Australian standards
1. 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.
(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.
(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.
(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.
(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?
2. Suppose you take out a loan of $10,000, repayable by five equal annual instalments. The interest rate is 10% per year.
(a) How much do you need to repay per year to the nearest cent if payments are due at the end of each year?
(b) What is the total amount of money repaid and how much of this are interest payments?
(c) It is often said that cash flow is one of the most important aspects in running a small business. If you were the manager of a small business and you made yearly repayments on a loan, would you rather make loan repayments at the beginning of each year or at the end of each year? Explain your answer.
3. Let $1000 be invested at the end of each year in perpetuity. The interest rate is 10% per year.
(a) Calculate the present value (PV) of the investment to the nearest cent after : (i) 1 year (ii) 10 years (iii) 50 years (iv) 100 years.
(b) Calculate the present value of the perpetuity. Explain why the present values in (a) approach the present value of the perpetuity as the number of years increases.
4. (a) Explain what is meant by the market capitalisation of a listed company. How would you find the market capitalisation of a listed company?
(b) If a company has 10,000,000 ordinary shares on issue with a current market price of $1.50 per share, calculate the market capitalisation of the company.
(c) The financial goal of a listed company is to maximise the shareholders’ wealth, by maximising the company’s share price. Is this the same as maximising the company’s profit? Explain your answer.
5. Suppose $10,000 is invested for 1 year at an interest rate of 6% per annum compounded.
(a) Calculate the future value (FV) if the compounding is performed quarterly. What is the effective annual rate of interest?
(b) Calculate the future value (FV) if the compounding is performed monthly. What is the effective annual rate of interest?
6. Suppose you bought shares in a listed company on the Australian stock market in March 2014 for $10,000, and you sold these shares for $15,000 in March 2016.
(a) What is the assessable capital gain from selling these shares?
(b) What is the net assessable capital gain that you will need to include in your tax return in Australia for the 2015-2016 financial year?
(c) If your marginal income tax rate is 37%, how much income tax will you pay on your capital gain for the 2015-2016 financial year? Do not include the Medicare Levy in your calculation.
7. Suppose $10,000 is invested at an interest rate of 8% per annum.
(a) Calculate the future value (FV) using simple interest if the term to maturity is 1 year.
(b) Calculate the future value (FV) using compound interest with annual compounding if the term to maturity is 1 year.
(c) Explain why the answers to (a) and (b) are the same.
(d) Calculate the future value (FV) using simple interest if the term to maturity is 2 years.
(e) Calculate the future value (FV) using compound interest with annual compounding if the term to maturity is 2 years.
(f) Explain why the answers to (d) and (e) are not the same.
8. Compound interest is a creator of wealth. A long-term outlook is required to make the most of the power of compounding. The following question is adapted from an article on page 38 in The Advertiser newspaper on Monday, February 6, 2017. A young investor starts depositing $200 per month at age 20, earning 8% per annum interest compounded monthly. She stops making deposits at age 30 and doesn’t touch her money until she retires at age 65. Her first deposit is on her 20th birthday and her last deposit is on her 30th birthday. Assume that her money continues to earn 8% per annum interest compounded monthly after she stops making deposits. Her friend starts to save at age 30 and deposits $200 per month until he retires at age 65. The investment also earns 8% per annum compounded monthly. His first deposit is on his 30th birthday and his last deposit is on his 65th birthday.
(a) How much does each investor deposit?
(b) Calculate the future (FV) of each investment using a financial calculator.
(c) Who has the larger amount of money at retirement? Why is it important to start investing at an early age?
9. Write a short essay to explain why the official interest rate is currently higher in Australia than most other places. Include a discussion of the Global Financial Crisis (GFC) in your answer. Also, explain why the Board of the Reserve Bank of Australia has the scope, if necessary, to further cut the cash rate, Australia’s official interest rate. Remember to give references in your references list at the end of your assignment.