Dixon Shuttleworth is offered the choice of three retirement-planning investments. The first investment offers a 5 percent return for the first five years, a 10 percent return for the next five years, and a 20 percent return the reafter. The second investment offers 10 percent for the first ten years and 15 percent thereafter. The third investment offers a constant 12 percent rate of return.

Determine, for each of the given number of years, which of these investments is the best for Dixon if he plans to make one payment today into one of these funds and to retire in the following number of years.

a. fifteen years

b. twenty years

c. thirty years.