1. Calculate the future value of an annuity for each of the following cases: - (a) RM3,000 per month for 5 years at interest rate 9% compounded monthly. (b) RM100,000 per month for 20 years at interest rate 7% compounded every year. (c) RM600 every 3 months for 7.5 years at interest rate 10% compounded 4 times in a year. 2. Calculate the present value of an annuity for each of the following cases: (a) RMS, 000 per year for a period of 8 years at interest rate 6% compounded every year. (b) RM1,200 every 6 months for a period of 6 years at interest rate 10% compounded every 2 times a year. (c) RMSOO per quarter for 7 years at interest rate 12% compounded quarterly. 3. Lucy bought a house worth RM490, 000. The bank has agreed to provide a loan with the following conditions Total loan: ' 90% of the house price Loan period: 25 years Loan interest rate: . 4. 25% compounded monthly _ Payment method: cash at the end of each month (a) What IS the amount of each payment at the end of each month that Lucy need to pay to the bank? (b) How much the balance of Luey's loan at the end of year 20'? 4. Darren has taken out a mortgage at a variable rate to nance the purchase of his house. The total loan is RMZSO, 000 for a period of 30 years, with an interest rate of 5.75% compounded. on a monthly basis Starting the 6th} gear, Darren' 5 mortgage will be revalued at an interest rate of 6. 95% compounded monthly (a) What is Darren's monthly payments at the rst 5 yeras? (b) How much the balance of Darren's loan at the end of year 5? (c) Starting at 6th year, how much is Darren's monthly payments