w-'" _'--'v ,. ' [TOTAL MARKS: 60 MARKS] PLEASE ANSWER ALL QUESTIONS. QUESTION 1 a) Give an expression for the present value with a nominal interest rate convertible monthly, 3 years before the rst payment is made for an annuity with payments of RM 400 every 4 months for 12 years: i) Expressed as an annuity-immediate (2 Marks) ii) Expressed as an annuity-due (2 Marks) iii) Haizal deposited RM 40.000 in a fund which is accumulating at 4% per annum convertible continuously. If Haizal withdraws some money continuously at the rate of RM 2400 per annum. how long can the fund last? (6 Marks) b) Due to the current COVlD-19 pandemic. Syail was one of those that got affected. She was given a choice by her employer to either resign with some compensation or to choose \"unpaid leave\" for quite sometime. She chose to resign and to receive the RM 500.000 as a compensation. She immediately purchases an annuity that will pay her with monthly payments for 5 years. with the rst payment made immediately. The effective rate of interest is 7% per annum. Find the monthly annuity payment that she will be receiving for 5 years. (7 Marks) c) Just before she started to receive her annuity payment in the 3"I year in (b). Syail was offered with a monthly perpetuity plan and would only start one month later. The new perpetuity payment is calculated based on the remaining balance of her compensation amount. The effective annual rate of interest is 9% per annum. i) Estimate the balance of her annuity plan right after receiving her 24\" payment. (2 Marks) ii) Indicate how much will Syail receive under her new monthly perpetuity plan