1. a) 8 marks Ted just won the lottery, and he must choose among three award options. He can elect to receive a lump sum today of $61m, to receive 10 payments of $9.5 million per year at the end of each year (the first payment occurs one year from now), or to receive 30 payments of $5.5 million per year at the end of each year (the first payment occurs one year from now).
   1. If he thinks he can earn 7% annually, which should he choose? (3 marks)
   2. If he thinks he can earn 9% annually, which is the best choice? (3 marks)
   3. Explain how interest rates influence the award options. (2 mark)
2. b) 7 marks You borrow $50,000 repayable in monthly instalments over 10 years. The nominal interest rate is 12% per annum. After 3 years have passed, the lender increases the interest rate to 13.5% per annum and you are given the choice of either increasing the monthly repayment or extending the term of the loan.
   1. What would be the new monthly repayment? (5 marks)
   2. What would be the new loan term? (2 marks) (Note: students may use the follow????????ing formula to solve for t)
   ????????= log(????????????????????????)

log(1 + ????????)

???????? = ???????????????????????????????????????????????? ???????????????? ????????????????????????????????????????????????; ???????? = ????????????????????????????????????????????????????????; ???????? = ???????????????????????????????????????????????????????? ????????????????????????????????????????; and ???????? = ???????????????????????????????????????????????????????????????? ????????????????????????????????.

c) 5 marks

Mickey is planning to save $50,000 per quarter for 10 years. Savings will earn interest at an (nominal) interest rate of 12% per annum. Calculate the present value for this annuity if interest is compounded semi-annually. (Note: students may try to convert the semi-annual rate to an effective annual rate, then to a quarterly rate)