Winifred has an opportunity to invest in Widgets USA. She can invest $100 today, which will return to her $60 at the end of 1 year and another $60 at the end of 2 years. (The original investment is not returned except through these future payments.)

(a) Suppose Winnie uses a 10% annual interest rate when discounting future payments. Calculate the present discounted value of this investment in Widgets USA.

Winnie learns of a second investment opportunity, this one in American Gadgets, which requires her to invest $80 today, and then in 1 year it pays off $90. (The original investment is not returned except through the future payment.)

(b) Calculate the (annual) internal rate of return on the investment in American Gadgets.

(c) For what nonnegative (annual) interest rates is the present discounted value of the Widgets USA investment larger than the present discounted value of the American Gadgets investment?