Question 2 (15 marks) You need to pay off a car loan within the next two years. The payment will be $4,000 every month. Today you have made a single deposit into a return-guaranteed investment account that will allow you to cope with all the monthly payments. This account earns an effective annual interest rate of 12.68250301%. The first payment will be made in one month. (a) Calculate the corresponding monthly rate for the investment account. (2 marks) (b) You need to have at least $96,000 (= $4,000 x 24) at your account today in order to make all the payments on the car loan in the next two years." True or false? Briefly explain without doing any time value of money related (i.e. PVA or FVA) calculations. (2 marks) (c) What is the size of the single deposit made today? (3 marks) (d) If your mother is going to make the first year's repayments for you (as a birthday gift) and thus you don't need to withdraw the $4,000 every month from the investment account, how much more money will you have in your bank account two years from now? (4 marks) (e) Suppose the (car) loan contract includes an alternative payment option that allows a lump-sum payment to be made at the end of Year 2 (instead of making monthly payments). What will be the size of the single repayment if the relevant interest rate is 1% per month? (4 marks)