You are working as a personal financial adviser. Alecia, one of your clients approached you for consultation about her plan to buy her dream house that costs $400,000. Alecia has a saving of $100,000 and is considering two alternative options:

Investment 1: Investing that $100,000 in an investment that would pay a rate of return of 9% annually, compounding semi-annually for 15 years.

Investment 2: Buying her dream house now. Then Alecia needs to borrow $300,000 mortgage from Prosperity Bank. The current interest rate the bank offered for the new mortgage is 4% annually, compounding monthly. The standard life of mortgage in Australia is 30 years.

Required:

a) Compute the effective annual interest rate (EAR) Alecia would actually get in Investment 1. (1 mark)

b) Calculate the amount of money Alecia would accumulate in Investment 1 after 15 years. (2 marks)

c) In Investment 1, how many year longer does Alecia need to wait until she has $400,000 to buy her dream house? (2 marks)

d) Calculate the monthly mortgage payment Alecia needs to pay for 30 years in Investment 2. (3 marks)

e) In investment 2, if Alecia leases the house to a company for a rent of $400 per week for 10 years, and put that rent in her bank account at the beginning of each week, how much money she will have in her bank account after 10 years if the interest rate is 3.5% annually, assuming compounding weekly? (3 marks)