Question 1:
a) 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 end-of-year payments of $9.5 million, or to receive 30 end-of-year payments of $5.5 million.
i. If he thinks he can earn 7% annually, which should he choose?
ii. If he thinks he can earn 9% annually, which is the best choice?
iii. Explain how interest rates influence the award options.
b) Today is your grandmother's 55th birthday. She plans to retire on her 65th birthday and wants to put aside the same sum of money every birthday (starting today) up to and including her 65th birthday. She then wants to be able to withdraw $10,000 every birthday (starting from her 66th) up to including her 85th birthday. She believes that an interest rate of 10% per annum is a reasonable estimate. How much does she need to put aside on each birthday?
c) 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. What would be the new monthly repayment? What would be the new loan term? (Note: students may use the following formula to solve for n)
d) 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.