You borrow R182 000 at an interest rate of K per year to by a new car to be paid off with 25 yearly instalments. You had financial trouble the first year so you only started making payments from year 2. The bank calculated that you need to pay R14 000 per year from year 2 to year 25. In year 17 you got a significant bonus and decided to use that money to make an R130 000 payment at the start year 18. Since you made a larger payment the bank recalculated your yearly payments now to be X per year starting in year 19. After having paid off the car you tell your friend how much you paid for your car over the 25 years. They also think it is a lot of money so you decide to consult the bank. They double-check their calculations and realise they made a mistake. To make up for it the bank will pay you a once-off settlement payment of R25 000 at the start of year 26. They also said that they will pay you the money they owe you starting in year 26. The bank starting in year 26 will pay you R2 300 and this amount will decrease year on year by 200 for the next 10 years. i) Draw a cash flow diagram of the situation described above? [3] ii) What is the NPV of the payments made from year 0 to the end of year 17? [2] iii) What is the NPV of the payments received from year 26 to the end of year 35? [4] iv) What is the NPV of the payments that you made from year 19 onwards? [2] v) what is the value of X? [3].

Inflation and interest rate K = 7.80%