When the mind is in the present moment, there are no problems because a problem always has some element of past or future. In the present moment, there is just a state of affairs. We are the ones who give that state of affairs a judgement by imposing onto it our fears and regrets. In order to be happy, we need to train the mind to let go of those fears and regrets and see the present moment for what it really is.
Therefore, if we train the mind through insight meditation to look at life as a collection of moments, we are training the mind to be free. As long as we remain attached to the past or the future, we are still waiting in the station. We are still looking for happiness to come to us in the form of external gratification. Once we bring the mind into the present moment and let go, we have bought the ticket to happiness which is an internal rather than external phenomenon. At that point, all we need to do is stay on the train of mindfulness and real happiness is inevitable.