(a) Suppose that you plan to buy a car for $8,000 in three years. Given a simple interest rate of 3% per annum on a savings account, how much capital do you need to invest today in order to buy the car in four years time? [5 marks]

(b) The first credit card that you get charges 11.4% interest to its customers and compounds that interest monthly. Within one day of getting your first credit card, you max out the credit limit by spending $1,000. If you do not buy anything else on the card and you do not make any payments, how much money would you owe the company after 6 months? [5 marks]

(c) An insurance company offers an ordinary annuity that earns 5.5% interest compounded annually. Mrs. Erna Smith plans to make equal annual deposits into this account for 30 years and then make 20 equal annual withdrawals of $ 28,000, reducing the balance of the account to zero.

(i) Compute the value of the fund based on the withdrawals required. [5 marks]

(ii) Compute the amount of each deposit needed in order to maintain the fund. [5 marks]

(iii) Compute the total interest earned over the entire 50 years. [5 marks]