IN TERMS OF FORMULAS

§10. Zero or Negative Rates of Interest

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terms of formulas all that is needed to make the rate of r '~binterest zero is that the forms of the F and <p functions Ia.

interest zero is that the forms of the F and <p functions fa.

shall be such as to produce this result. This implies that +t.

khC(>A'^C'

fa

these functions shall have solution values equal to zero. «'*-

Of course it would be possible that interest, impatience, t

and return over cost for one particular year might be zeroor negative without this being true for other years. If they llwere zero for all the years, we should have the interesting Iresult that the value of a finite perpetual annuity (greater •;than zero per year) would be infinity. No one could buya piece of land for instance, expected to yield a net income 1forever, for less than an infinite sum. A perpetual govern-ment bond from which an income forever was assuredwould have an infinite value. Since this is quite imprac-ticable, we thereby reduce to an absurdity the idea thatit is possible to have at one and the same time:

1. A zero rate of interest for each year forever; and

2. a perpetual annuity greater than zero per year.

But the absurdity is lessened or disappears altogether

if either:

1. The zero rate of interest is confined to one year; or ^

2. no perpetual annuity greater than zero per year ispossible.

Unusual conditions may easily reduce the rate of in-terest for one year to zero. As to an unproductive orbarren world, like the hard-tack island, only a finitetotality of income would be possible; a perpetual an-

nuity even of one crumb of hard-tack a year would be . ^impossible.

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