Suppose we have a graph whose axes are r (interest rate) and S/I/Y/whatever. I'm studying intertemporal models right now, and i got a bit confused. According to my textbook, the area underneath S is the cost of savings (forgone current consumption), and the area underneath I is the returns on investment. After some digging, i think i've figured out the latter (investment curves are sums of individual corporate investment portfolios sorted from the largest to smallest in terms of returns, where the y (or r, in this case) axis is expected rate of returns). But what I don't get is the former - why is the area underneath the S curve the cost of saving?
*I understand why changing interest rates affect savings, both through the substitution and income/wealth effect, but that's not really helping me interpret the graph.