Earning a return on capital --------------------
How can we describe how capital C changes over time? Two models coexist and remain in use despite their well-documented shortcomings.
Thus, C(t) = C(0) × (1 + it) in the simple-interest model, where t is the time elapsed since a reference date—the date on which the capital is known—and i is the interest rate, or equivalently the return per unit of capital per unit time.
The exponential model, meanwhile, comes in two forms: compound interest, with C(t) = C(0) × (1+i)*t, and continuous compounding, where C(t) = C(0) × exp(rt), with r* denoting the instantaneous rate of return per unit of time and capital.
Banking practices have also given rise to a hybrid model that combines simple and compound interest by recapitalizing at arbitrarily chosen times. One such model of capital growth over time consists of a series of line segments that form chords of the exponential curve and, by convexity, lie above it.