<p>A classic inequality from interest theory states that the nominal annual rates of interest decrease with the number of compounding periods. We provide a novel constructive proof by first relating the nominal rates to cashflows and then establishing their ordering by showing that a natural algorithm to move individual amounts constituting one such cashflow to form the other is value increasing. Our algorithm admits a probabilistic interpretation, and the ease of establishing the value-increasing property relies on a related bivariate distribution having the martingale property. We also show, using optimal transport theory, that our algorithm is minimal in terms of two financially meaningful transport costs. Finally, our analysis provides an actuarial example of a comonotonic distribution that has the martingale property.</p>