Question 1 (12 marks) (a) Suppose you want to save for your retirement in an account that can earn an annual rate of return of 7.5 percent. (i) You have just made your first $10,000 contribution to your retirement account. What will your account be worth when you retire in 40 years, assuming you make no additional contributions? Show your calculations. + (3 marks) In addition to your first $10,000 contribution, what will your account be worth when you retire in 40 years, if you deposit $4,000 at the end of each year for the next 40 years? Show your calculations. (3 marks) (b) Suppose you want to buy a new laptop which costs $15,000. The store will allow you to make monthly instalments for 3 years, and the interest rate is 5.5% with monthly compounding. The monthly payment is made at the beginning of every month. What is your monthly payment? Show your calculations. (3 marks) (c) Suppose you are considering taking a loan from one of two financial companies. Financial Company X charges you an interest rate of 13.5% with monthly compounding. Financial Company Y charges you an effective annual rate (EAR) of 14% with semi-annual compounding. Which company should you borrow your loan from and why? Show your calculations