(a) Explain what is meant by a perpetuity. State and derive a formula for the present value of a perpetuity. [6] (b) 2 years ago, you bought a car worth 30,000 and you paid a 10% deposit at that time and borrowed 90% from the bank with an annual interest rate of 8.5%. You decided to pay this car loan in equal instalments every month for 9 years. Assume the interest rate is constant through the life of the loan. Please answer the questions below: (i) What is your monthly repayment? [5] (ii) What is your current outstanding balance of the car loan immediately after the instalment paid at the end of year 2? [4] (iii) You want to pay less interest, and decide after the instalment paid at the end of year 2 that you want to start paying fortnightly, instead of monthly. How much will the fortnightly payment be? [4] (c) Find the rate of continuous compounding equivalent to (i) monthly compounding at 8.5%. [3] (ii) fortnightly compounding at 8.5%. [3]