8.2 A man invests a certain amount of money into an account. Interest is 12% per annum compounded monthly for the first two years and 14% per annum compounded quarterly for the remaining time. Five years after the initial investment, he needs to withdraw R 10000 to do some renovations on his house. Seven years after the initial investment, he had R80 312,55. Calculate the amount of money he invested initially. 8.3 Determine how many years it would take for the value of a car to depreciation to 50% of its original value, if the rate of depreciation, based on the reducing-balance method is 8% per annum. 8.4 Jeremy took out a home loan for R500 000 at an interest rate of 12% per annum compounded monthly. He plans to repay this loan over 20 years and his first payment is made one month after the loan is granted. 8.4.1 Calculate the value of Jeremy's monthly instalment. 8.4.2 Calculate Jeremy's balance outstanding after his 10th payment 8.4.3 Mary took out a loan for the same amount and at the same interest rate as Jeremy. Mary decided to pay R6 000 at the end of every month. Calculate how many months it took for Mary to settle the loan. 8.4.4 Who pays more interest, Jeremy or Mary? Justify your answer. 8.5 A vehicle is bought at the beginning of the month. It is to be replaced at the end of 4 years from the time of purchase. This vehicle will be used as a trade-in. the cost of a new vehicle is estimated to be R614490,66. A sinking fund is created to cover the replacement cost of this vehicle. Monthly payments will be made at the end of each month. The first payment will be made on the day of purchase of the vehicle and the last payment will be made at the end of the four-year period. The sinking fund earns interest at a rate of 6,2% per annum compounded monthly. Calculate the monthly payment to the fund. [30] NB: Under NO circumstances will late (after 07h45) assignments be accepted, PERIOD