Magnus, just turned 32, is a freelance web designer. He has just won a design project contract from AAA Inc. that would last for 3 years. The contract offers two different pay packages for Magnus to choose from: Package 1: $30,000 paid at the beginning of each month over the three-year period. Package II: $26,000 paid at the beginning of each month over the three years, along with a $200,000 bonus (more commonly known as "gratuity") at the end of the contract. The relevant yearly interest rate is 12.68250301%. a) Which package has higher value today? [Hint: Take a look at the practice questions set IF you have not done so yet!] (14 marks) b) Confirm your decision in part (a) using the Net Present Value (NPV) decision rule. (4 marks) c) Continued from part (a). Suppose Magnus plans to invest the amount of income he accumulated at the end of the project (exactly three years from now) in a retirement savings plan that would provide him with a perpetual stream of fixed yearly payments starting from his 60th birthday. How much will Magnus receive every year from the retirement plan if the relevant yearly interest rate is the same as above (12.68250301\%)? (7 marks) Question 2 (13 marks) To pay off your loan, you are required to make payments of $1,000 per month in the first year and payments of $1,500 every month during the second and third years. The investment account from which you will withdraw to pay for the loan earns an interest rate of 6% compounded monthly. The first payment begins in one month. a) How much money do you need to have in your investment account now to pay off the loan (according to the repayment schedule of the loan contract)? ( 9 marks) b) If you do not have to make the second year's payments (someone is paying for you) and thus you can leave the money in the investment account to carn interest. How much more money will you have at the end of Year 4? (4 marks) Question 3 (12 marks) Larissa borrowed $8 million and planned to repay the loan by making equal month-end payments over a period of 10 years. The interest rate on the loan is 4.8%, compounded monthly. a) Determine the size of the monthly payments. (4 marks) b) Of the 72nd payment, how much are used to repay the principal and the interest payment for the month respectively? (8 marks)