xBookUtils.terms['fn_14_501'] = "The words “investment” and “investing” are often used in casual conversation to describe individuals and firms saving money through banks, brokers, and other financial institutions. This isn’t exactly what economists usually mean when they use these words; the economic definition implies the purchase of some sort of capital with the hope of a future payoff. As we see later in the chapter, however, savings and investment (by the economic definition) are, in fact, linked. This connection results from the functioning of capital markets. Essentially, savers provide funds that investors use to purchase capital. The investors compensate the savers by paying back some of the investment’s returns.";
xBookUtils.terms['fn_14_502'] = "Some people use the “Rule of 70” instead; it works the same way. The Rule of 70 is slightly more accurate, but the Rule of 72 is often used for convenience, because so many numbers divide into it evenly. For you math fans out there, the reason the Rule of 72 (or 70) works is that the size of initial value A growing at a constant rate r over a time period t is X = Aert. If we replace X with 2A (to represent a doubling of the initial value) and take the natural log of both sides of the equation, we have rt = ln 2. Since ln 2 ≈ 0.70, substituting and solving give t ≈ 0.70/r (that’s why the Rule of 70 is a slightly better approximation).";
xBookUtils.terms['fn_14_503'] = "An important detail when calculating PDVs is to make sure the interest rate r matches the period t. That is, if t is expressed in years, annual interest rates should be used. If t is instead, say, months, then monthly interest rates should be used (and if necessary, converted from whatever time basis they were originally expressed in).";
xBookUtils.terms['fn_14_504'] = "This example is based on an actual decision United faced at the time. We picked the dollar values in the example to be realistic, but we don’t know what United actually paid. Furthermore, to keep things simple, we’ve ignored many other aspects of the plane-replacement problem that matter in real life, such as flyers’ willingness to pay to fly on newer aircraft, the interactions between United’s plane choice and its contracts with its unions, and so on.";
xBookUtils.terms['fn_14_505'] = "This became known as the Fisher rule, in honor of the early-twentieth-century Yale economist Irving Fisher. It derives from the fact that any principal amount A earning a nominal interest rate of i will be worth A × (1 + i) in non-inflation-adjusted terms. If the inflation rate over the period is π, then money that could buy A worth of goods at the beginning of the period can buy A/(1 + π) at the end of the period. So, the real value of the principal at the end is A × (1 + i)/(1 + π). The real interest rate is the percentage change in purchasing power over the initial principal’s purchasing power: r = [(A(1 + i)/(1 + π)) – A]/A = (1 + i)/(1 + π) – 1 = (i – π)/(1 + π). If π isn’t very high, that’s approximately equal to i – π.";
xBookUtils.terms['fn_14_506'] = "Many factors can affect these probabilities in actual investment choices. Sometimes probabilities are objectively defined; that is, they are verifiably exact. An example is the outcome of flipping a coin: Everyone knows there is exactly a 50% chance of either a head or tail. Another example is a state lottery game that promises 10% of all cards are winners. You know that 1 out of every 10 cards will be a winner. In most real-world investment scenarios, however, probabilities are not objective, but subjective. That is, they are determined by the decision maker’s judgment rather than set in stone by the fact that a coin only has two sides or that an accounting firm has verified the lottery’s procedures. With subjective probabilities, knowing which factors affect the possible outcomes helps a decision maker. We’re not going to worry about the distinction between the two types of probabilities here—we keep it simple and assume all the probabilities we discuss are objectively defined—but it’s worth remembering the difference in practical situations.";
xBookUtils.terms['fn_14_507'] = "Insurers often make money one other way. They invest the premia paid by their policyholders and earn interest on those investments during the time between when they collect the premia and have to pay out claims.";
xBookUtils.terms['fn_14_508'] = "Amy Finkelstein and Robin McKnight, “What Did Medicare Do? The Initial Impact of Medicare on Mortality and Out of Pocket Medical Spending,” Journal of Public Economics 92, no. 7 (2008): 1644–1668.";