Shahriza's mother wishes to invest some money now in an investment plan, that pays 9% interest per year. The amount from the plan will be used only to pay for Shahriza's college programme, which starts now. The initial registration fee of RM4,000 must be paid now. The college tuition fees are roughly RM12,000 per year for four years and must be paid up-front, at the start of each year. Completion and graduation fees of RM3,000 must be paid at the end of four years.

(a) How much must then be invested in the investment plan now? (3 marks)

(b) If the investment plan's interest is compounded quarterly rather than yearly, and the college tuition fees are RM6,000 paid at the start of each term of 6 months, rather than RM12,000 paid at the start of each year, what is the effective interest rate earned every 6 months from the above investment plan? (2 marks)

(c) Given the condition in (b) above, if Shahriza's mother invests only RM40,000 now in the investment plan, how much must she invest in the plan at the end of 3 years, so that the amount in the plan is ju enough to cover all fees? (5 marks)