1. The annually compounded discount rate is 13.5%. You are asked to calculate the present value of a 16-year annuity with payments of $51,800 per year.

a. Calculate the PV if the annuity payments arrive at one-year intervals. The first payment arrives one year from now. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. Calculate the PV if the first payment arrives in six months. Following payments arrive at one-year intervals (i.e., at 18 months, 30 months, etc.). (Do not round intermediate calculations. Round your answer to 2 decimal places.)

2. The $43 million lottery prize that you have just won actually pays out $3.5 million a year for 20 years. The interest rate is 8.0%.

a. If the first payment comes after 1 year, what is the present value of your winnings? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

b. What is the present value if the first payment comes immediately? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)