3. (a) Suppose that you plan to buy a boat for €10,000 in three years. Given a simple interest rate of 4% per annum on a

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3 A Suppose That You Plan To Buy A Boat For 10 000 In Three Years Given A Simple Interest Rate Of 4 Per Annum On A 1 (157.31 KiB) Viewed 17 times

3. (a) Suppose that you plan to buy a boat for €10,000 in three years. Given a simple interest rate of 4% per annum on a savings account, how much capital do you need to invest today in order to buy the boat in three years time? [4 marks) (b) Maria inherits the sum of €200,000. She wishes to invest some of this money so that in 15 years time her investment will have grown to €300,000. Her bank has recommended an account which offers an interest rate of 12% per year compounded semi-annually. How much of her money should she invest? [5 marks] (c) A company estimates that it will need to replace a piece of equipment at a cost of €50,000 in 5 years. To have this money available in 5 years it establishes a sinking fund by making equal monthly payments into an account paying 6.6% per annum compounded monthly. (i) How much should each payment be? [5 marks] (ii) How much interest is earned during the 5 years? [3 marks] (d) At the time they retire, a couple has € 200,000 in an account that pays 6.5% interest compounded annually. (i) If the couple decides to withdraw equal yearly payments for 15 years, at the end of which the account will have zero balance, how much should the couple withdraw each year? [5 marks] (ii) Compute the total interest earned over these last 15 years.