This volume opens the third of the fundamental prices. After the price of labour and the price of position comes the price of time — interest, the premium the present commands over the future, the discount that makes a good tomorrow worth less than the very same good today. This first plate establishes the phenomenon itself, the discount, before the plates that follow ask why it exists and who fixes its size. It will show that the future is, universally and measurably, valued below the present; that the interest rate is the measure of that discount, the exchange rate between today and tomorrow; that this one rate, compounded, governs the worth of everything that has a future — the bond, the mortgage, the pension, the share, the insurance, the debt of nations; and that the volume's running question, whether the price of time is the just reward of waiting or the moneylender's toll upon need, begins in the simple and strange fact that time itself should have a price at all.
Begin with the fact, which is so familiar that its strangeness is easily missed. Offered a good thing now, or the very same good thing a year hence — a sum of money, a measure of grain, a pleasure — nearly everyone, nearly always, prefers it now. The future good is discounted: it is worth less, to us today, than the identical present good. This is not because the future good is any different, for it is by stipulation the same; nor only because we may not live to enjoy it, though that plays its part; but because of something deep in the way the present and the future are weighed against one another. A bird in the hand is worth more than the same bird in the bush a year off; and the amount by which it is worth more — the premium upon having it now — is the seed of interest. The lender who parts with a good today, surrendering the present's premium, must be paid to do so; and the payment, the excess of what is returned over what was lent, is interest: the price of the time for which the good was given up.
What the interest rate does is measure this discount — to put a number on the premium of the present. If a sum lent today must be returned with five in the hundred added in a year, then the rate of interest is five per cent, and it says precisely how much more a present good is worth than the same good a year off: a hundred now is worth a hundred and five then, or, read the other way about, a hundred a year hence is worth only some ninety-five and a quarter today. This second reading is the more powerful, and it is the master tool of all of finance: the present value of a future sum — what a payment due tomorrow is worth today — found by discounting it at the rate of interest. Every future payment, divided by one plus the rate (and, for payments further off, by one plus the rate again and again, once for every year of waiting), shrinks to its present worth. The interest rate is thus the hinge on which the present and the future swing: raise it, and the future shrinks, every distant payment worth less today; lower it, and the future swells, the same payments worth more. The rate is the exchange rate between the two countries of time, and present value is the conversion that it performs.
The rate is the exchange rate between the two countries of time, and present value the conversion it performs.
And upon this single operation — the discounting of the future to the present — the whole edifice of finance is raised. For nearly everything of value is a claim upon the future: the bond that promises payments in the years to come, the mortgage repaid across decades, the share that entitles its holder to a stream of distant profits, the pension that will pay out in old age, the factory that will yield its returns over its working life. To value any one of these is to do a single thing: to take each of its future payments, discount each to its present worth at the rate of interest, and add them together. The value of any asset whatever is the present value of the future it promises — the fundamental equation of which all the rest of finance is only the commentary. And because the interest rate is the discounter, it is the secret governor of every such value: when the rate falls, all these future-laden things grow dearer at once — bonds, houses, shares, the whole of them — for their distant payments are now discounted more gently; when it rises, they all grow cheaper together. The mysterious sympathy by which a single change in a single rate moves every market at once is, in the end, no mystery at all: it is the discount, at work everywhere the future is bought and sold.
One feature of the discount deserves a plate to itself, and will have to make do with a passage: that it compounds. Interest is paid not only upon the original sum but, in time, upon the interest already added — interest upon interest — and so a sum left to grow does not climb in a straight line but curves upward, ever more steeply, in the exponential ascent that is the most powerful and least intuitive force in all of finance. A modest rate, given time enough, works wonders: a sum at seven in the hundred doubles in a decade, and multiplies some thirtyfold in half a century. This is the saver's friend, the slow magic that turns patient thrift into a fortune. But the very same exponential, run in reverse, is the discounter's blade. For if compounding swells the present sum into the future, it makes the future sum dwindle, and just as fast, into the present: at seven per cent, a fortune promised a century hence is worth, today, less than a hundredth part of itself. The far future, discounted at any ordinary rate, shrinks almost to nothing in present value — a fact of no consequence whatever for a one-year loan, and of the gravest consequence for the things that reach across the generations, the fate of the climate above all, to which a later plate must return. The same curve that enriches the saver annihilates the distant future; and which of its two faces it shows depends only on which way through time one reads it.
But why should the future be discounted at all? Why is a good tomorrow worth less than the same good today — what is the premium on the present a premium for? Here this plate must point ahead rather than answer, for the question is the very matter of the two plates that follow. There are, in the long debate, two great answers, and they are not so much rivals as the two blades of a single pair of shears. The first looks to the mind of the one who waits: that we are, quite simply, impatient — that we prefer our satisfactions sooner than later, by some quirk of temperament, or failure of imagination, or rational regard for an uncertain and mortal life, and so must be paid to defer them. The second looks to the world the waiting acts upon: that resources today are productive — that a good in hand can be set to work, planted or built or invested, to yield more than itself in time, so that present goods are worth more than future ones because they can be made into more future goods than the future would otherwise hold. Impatience pulls the rate up from the side of demand, and productivity holds it up from the side of supply; and the rate we actually observe is set where the two of them meet.
Impatience pulls the rate up from the side of demand, and productivity holds it up from the side of supply; the rate we observe is set where the two of them meet.
And here, at the foundation, the volume's running question must be planted, though it cannot yet be answered. For to say that the future is discounted, and that interest is the price of the discount, is to say that interest has a real basis — that it is not, or not merely, an imposition wrung from the weak by the strong, but the price of a genuine thing, the premium the present really does command over the future. In this, interest is no different from the rent of the volume before: it answers to a real phenomenon, as the rent of land answered to a real scarcity. And yet — the volume's scruple, present from its first plate — that the discount is real does not in the least settle that any given interest charge is just. For the size of the discount is fixed by no law of nature; it varies with impatience and productivity, with the supply of savings and the will of the central bank, as the later plates will show, and a rate may be driven, by a lender's power over a borrower's need, far above the true premium of time, into the territory the old moralists damned as usury. The discount is real; the rate is contingent; and whether a particular price of time is the fair reward of waiting or the toll of the strong upon the desperate is the question this volume, like the two before it, exists to hold open — the same seam between the earned and the extracted, running now through the price of time. The reality of the discount establishes that interest can be earned; it does not establish that any given interest is.
So the volume of the rate begins where it must, with the bare fact that time has a price. A good tomorrow is worth less than the same good today; the interest rate measures by how much; present value, the discounting of the future at that rate, is the operation by which the worth of everything to come is found; and compounding, the same operation run again and again, both grows the saver's hoard and shrinks the distant future toward nothing. Why the discount exists — impatience, productivity, or the two together — the next plates will take up; how the rate is set — by the market, by money, by the central bank — the plates after those; and whether the price of time is ever unjust — the ancient charge of usury — a plate all its own. But the whole of it begins here, in the premium the present commands over the future, the strange and universal fact that we would simply rather have the good thing now. The price of time is the most pervasive price there is, for it is folded into every other — every wage deferred, every rent capitalized, every venture weighed — and it is, like every price in this table, a verdict upon a contest: between the present and the future, between the one who can wait and the one who cannot, between the real premium of time and the power to charge beyond it. As the table says of every price within it, the argument remains open.