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In a 1992 Virginia lottery, the jackpot was $27 million. An Australian investment firm tried to buy all possible combinations of numbers, which would have cost $7 million. In fact, the firm ran out of time and was unable to buy all combinations but ended up with the only winning ticket anyway. The firm received the jackpot in 20 equal annual payments of $1.35 million. Assume these payments meet the conditions of an ordinary annuity.

A) Suppose the firm can invest money at 8% interest com-pounded annually. How many years would it take until the investors would be further ahead than if they had simply invested the $7 million at the same rate? (Hint: Experiment with different values of n, the number of years, or use a graphing calculator to plot the value of both investments as a function of the number of years.)

B) How many years would it take in part (a) at an interest rate of 12%?