Congratulations on the new arrival!!! Your newborn will be going to college 18 short years from today, so you will need $1,000,000 at that time to fund the child's education. Each investment earns the same APR. Which of the following would result in your investing the fewest total dollars to arrive at the same $1,000,000 in eighteen short years?

a. Investing a single lump sum today

b. Investing at the end of each year

c.Investing at the beginning of each month

d. Investing at the beginning of each year

You just won the lottery. You selected the "cash option" where the Lottery Board will pay you one lump sum today as opposed to paying you some amount at the end of each year for the next 20 years (your prize is the present value of an ordinary annuity). Which of the following is true: Everything else equal.

a. Your lump sum prize will be larger if the Lottery Board uses a higher discount rate.

b. Your lump sum prize will be smaller if the Lottery Board uses a higher discount rate.

c. Your lump sum prize will be the same regardless of the discount rate used.

d. We do not know how a higher or lower discount rate would affect your prize since we don't know the exact discount rate.