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

Kate would like to invest a certain amount of money for three years and considers investing in $(1)$ a one$-$year bond that pays $3$ percent, followed by a two$-$year bond that pays the forward rate, or $(2)$ a three$-$year bond that pays $8$ percent in each of the next three years. Kate is considering the following investment strategies:

Strategy A: Buy a one$-$year bond that pays $3$ 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 $8$ percent in each of the next three years.

If the two$-$year bond purchased one year from now pays $9$ percent annually, Kate will choose Strategy A or Strategy B$.$

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

The rate on the two$-$year bond purchased one year from now is $10\mathrm{.}590$ percent.

The rate on the two$-$year bond purchased one year from now is $11\mathrm{.}120$ percent.

The rate on the two$-$year bond purchased one year from now is $11\mathrm{.}543$ percent.

The rate on the two$-$year bond purchased one year from now is $9\mathrm{.}743$ percent.