Question 1 (Total marks for this question = 10 marks)

Suppose \$1,000 is invested each year for 5 years at an interest rate of 10% per annum compounded.

• Calculate the future value of the investment if the payments are invested at the end of each year and the compounding is annual compounding. (2 marks)
• Calculate the future value of the investment if the payments are invested at the beginning of each year and the compounding is annual compounding. (2 marks)
• Calculate the future value of the investment if the payments are invested at the end of each

year and the compounding is monthly compounding. (2 marks)

• Explain what is meant by continuous compounding. (2 marks)
• Calculate the future value of the investment if the payments are invested at the end of each year and the compounding is continuous compounding. (2 marks)

Question 2 (Total marks for this question = 10 marks)

You would like to have \$100,000 in 10 years from now to fund the education expenses of a family member. You wish to deposit money into a bank account to achieve this goal. The money will earn interest at 3% per annum compounded annually.

• How much must you deposit annually as an ordinary annuity to achieve your goal? (3 marks)
• Instead of making annual deposits, how much would you need to deposit as a lump-sum today to reach your goal? (3 marks)
• Suppose that at the beginning of the first year, you deposit \$10,000 in the bank towards your goal of \$100,000 at the end of 10 years. In addition to this deposit, how much must you deposit each year as an ordinary annuity to obtain your goal? (4 marks)

Question 3 (Total marks for this question = 12 marks)

An investor wishes to invest \$10,000 in a term deposit with a bank for a term of 2 years. The bank is offering term deposits with an interest rate of 3% per annum with annual compounding, or an interest rate of 2.95% per annum with half-yearly compounding, or an interest rate of 2.9% per annum with quarterly compounding.

• Which term deposit is the best investment? (3 marks)
• Calculate the future value (FV) of each of the three investments. (6 marks)
• If the marginal income tax rate for the investor is 45%, what is the total amount of interest received after tax for each of the three investments? (3 marks)

Question 4 (Total marks for this question = 8 marks)

An employee of a company wants to accumulate \$1,000,000 to be able to retire. The employee wants to deposit money on a regular basis into their investment account.

• Suppose the employee deposits \$5,000 at the end of each year into their investment account. With annual compounding, what annual percentage rate will need to be earned for the employee to be able to retire in 25 years after opening their account? (2 marks)
• Assume the employee deposits \$100,000 at the beginning of the first year into their investment account and deposits \$5,000 at the end of each year. With annual compounding, what annual percentage rate will need to be earned for the employee to be able to retire 25 years after opening their account? (3 marks)
• If the employee deposits \$5,000 at the end of each year into their investment account, how long would it take for the employee to accumulate \$1,000,000 to be able to retire assuming an interest rate of 10% per annum with monthly compounding? (3 marks)

Total Marks for Assignment Part A = 40 Marks

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