Ariff has three children, Afrina, Ayra and Atilia. Ariff is making financial plans for his three children so that they can continue their studies at university without facing any financial problems.

Afrina is now 5 years old. Ariff needs to make sure that there is RM60,000 in Afrina's account when she is 18 years old.

Ayra is now 2 years old. Ariff will keep RM1,500 every year for eight years starting next year into his account. When at university, Ayra will spend RM14,400 every year for four years starting when she is 17 years old.

When Atilia was one year old, Ariff had deposited RM15,000 into his account. There is now RM35,000 in his account.

a) How much should be saved at the beginning of each year for five years so that there is RM65,000 in Afrina's account when she is 18 years old. Assume the annual interest rate is seven percent.

(2.5 marks)

b) Ariff realizes that the savings made into Ayra's account is not enough if Ayra has to spend RM14,400 every year for four years starting when she is 17 years old. How much additional amount will need to be deposited next year to enable Ayra to do so? Assume the annual interest rate is seven percent.

(6 marks)

c) How old is Atilia today? Assume that the annual interest rate is seven percent compounded twice a year.

(3.5 marks)

d) Explain the relationship that exists between future value, interest rate and period.

(4 marks)

e) What is the difference between a regular annuity and a mature annuity? What is meant by perpetuity? Give an example of perpetuity.

(4 marks)