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Alice has $5 000 now. She wants to save $25 000 to buy her first car. She decides to put that $5 000 in an investment fund that pays an interest rate of 10% per annum (per year), compounding annually.

Required:

a) How long does Alice need to wait until she has saved $25 000? (2 marks)

b) If Alice wishes to have that $25 000 in five (5) years, how much does she need to put into the investment now with the same interest rate of 10%? (2 marks)

c) Assume that Alice was offered an alternative investment, which requires an initial investment of $6 000 for seven (7) years. Calculate the amount of money that Alice would accumulate after seven (7) years, if the rate of return is 12%, compounding quarterly. (2 marks)

d) Assume that Alice was offered two (2) other alternative investments in the securities market: i. Option A pays an interest rate of 10% p.a. (per year), compounding semi-annually. ii. Option B pays an interest rate of 9.87%, compounding monthly. Which option (A or B) should Alice choose? (2 marks)

e) Assume that Alice has achieved her goal of $25 000 as a deposit and now she wants to purchase a car which costs $45 000. Her plan is to pay $25 000 in cash and finance the balance over three (3) years at an interest rate of 3.5%. What will be her monthly payment? (2 marks)

f) At the end of this year, Alice will receive a fixed income of $10,000 each year forever. If the required rate of return is 14%, what is the present value of this income flow? (1 mark)

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