When allowing interest rates to vary, the branch from node $($n$,$j$)$

to $($n$+1,$j$+1)$

and the branch from node $($n$,$j$)$

to $($n$+1,$j$)$

have the same return because

a$.$bank investments are not risky and don$$t change so quickly.

b$,$he probability of going into the upstate is the same as going into the downstate.

c$,$we don$$t want to make our model too complicated.

d$,$there are regulations controlling the rate of return and only one is allowed.