Riskless profit from two continuously compounded accounts

Two bank accounts both start at value $1$: account $B_1$ grows at a continuously compounded $4\%$ per year and account $B_2$ at $2\%$. You start with no money, and you may only deposit into or borrow from each account in whole units; simply depositing your own cash is not an option. What is the smallest profit you can lock in after one year? Give two decimal places.

About $0.02$. Borrow one unit from the $2\%$ account and deposit it in the $4\%$ account. After a year you hold $e^{0.04}$ and owe $e^{0.02}$, a riskless gain of $e^{0.04}-e^{0.02}\approx0.0206$.