(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)

(ii)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 CompanyXcharges you an interest rate of 13.5% with monthly compounding. Financial CompanyYcharges 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.