Question 1 Assume that you just won the government vaccination lottery. Your prize can be taken either in the form of $100,000 at the end of each of the next 20 years (i.e., $2 million over 20 years) or as a lump sum of $1,000,000 paid immediately. (a) If you expect to invest $100,000 annually that earns 6% annually on your investments over the next 20 years, calculate the current value of future payments from an annuity. Explain how you would use time value of money analysis to choose between the annuity and the lump sum. [within 50 words] (5 marks) (b) If you expect to invest $100,000 annually that earns 8% annually on your investments over the next 20 years, calculate the current value of future payments from an annuity. Explain how you would use time value of money analysis to choose between the annuity and the lump sum. [within 50 words] (5 marks) (c) Using interpolation based on your answers in part (a) and (b), at approximately what interest rate would you be indifferent when choosing between the two plans? (2 marks) (d) You can earn 3 percent, compounded monthly at your bank. If you deposit $1,000,000 at age 28, how old will you be when your account has grown to $2,000,000? What is the effective annual rate? (6 marks)