This is commonly handled is what is referred to as a rollover. This is generally done transparently, but it does mean that at the end of each day you will either pay or receive the interest differential on your position.
The type of trader you are and the way your broker handles rollover will be the deciding factors in determining whether the interest rate differentials are an important concern for you. Some brokers will not apply the day's interest differential value on positions closed out during the trading day.