$5.$ Pure expectations theory: Multi$-$year periods

Cho would like to invest a certain amount of money for three years and considers investing in $(1)$ a one$-$year bond that pays $4$ percent, followed by a two$-$year bond that pays the forward rate, or $(2)$ a three$-$year bond that pays $9$ percent in each of the next three years. Cho is considering the following investment strategies:

Strategy A: Buy a one$-$year bond that pays $4$ percent in year one, then buy a two$-$year bond that pays the two$-$year forward rate in years two and three.

Strategy B: Buy a three$-$year bond that pays $9$ percent in each of the next three years.

If the two$-$year bond purchased one year from now pays $7$ percent annually, Cho will choose $.$

Which of the following describes conditions under which Cho would be indifferent between Strategy A and Strategy B$?$

The rate on the two$-$year bond purchased one year from now is $11\mathrm{.}589$ percent.

The rate on the two$-$year bond purchased one year from now is $12\mathrm{.}168$ percent.

The rate on the two$-$year bond purchased one year from now is $12\mathrm{.}632$ percent.

The rate on the two$-$year bond purchased one year from now is $9\mathrm{.}967$ percent.