You have $50,000 saving and are considering a 30-year investment which is offered in two phases:

Phase 1: Investing that $50,000 as a lump sum in an investment in the securities market for 20 years. Your securities broker recommends two alternative options: Option A pays interest rate of 11.87%, compounding daily. Option B pays interest rate of 12%, compounding quarterly.

Phase 2: At the end of 20 years, putting the total amount accumulated in the first phase into another investment, which will pay you an equal income at the end of each year for 10 years.

a) Identify which option should you choose in Phase 1 by computing the effective annual interest rate (EAR)? (2 marks)

b) Calculate the amount of money you would accumulate in Phase 1 after 20 years if you choose Option A? (2 marks)

c) If you would like to have exactly $600,000 after 20 years, how much the investment rate of return (compounding annually) should be? (3 marks)

d) Assume that after 20 years, you put totally $500,000 in the investment in Phase 2, calculate the amount of yearly income would you receive each year for 10 years if the required rate of return is 12.5%, compounding annually? (2 marks)

e) In phase 2, assume the payment of income is changed to 74,000 per year forever. Calculate the rate of return would you get from the investment? (2 marks)