Question 3 (25 marks)

Mr Tan saves regularly over the last 5 years after graduating from university. Today, he has $16,000 savings. He establishes his retirement fund in 5 years and feels he needs$100,000 to do so. Assume annual compounding.

a) If he could make 12% p.a. from his investment, how much his $16,000 savings is worth at the end of 5-year? Does Mr Tan have $100,000 he needs? How much more he needs today to achieve his goal? (10 marks)

b) How much Mr. Tan need to invest at the end of each year over the next 5 yearsto make up his shortfall in (a), assuming he can earn an interest rate at 12% p.a.? (8 marks)

c) If Mr Tan saves an additional $2,000 a year on top of his lump-sum savings, does he have $100,000 enough for his retirement sum in year 5? What return MrTan should seek to grow his savings of $16,000 to $100,000 over 5 years? If he invests all his savings in an investment generating 12% p.a., how long MrTan could achieve his retirement fund? (7 marks)