In this paper, we consider a problem that is due to Bruno De Finetti. The risk is described as the classical risk process with constant interest force. Dividends are paid according to a constant dividend barrier strategy. When the process reaches the barrier, all the premium income no longer goes into the surplus but is paid out as dividends to shareholders. Using the Markov property of the risk process, we obtain the explicit expression for the expectation of aggregate discounted dividends until ruin.