244 NATURE OF CAPITAL AND INCOME [CHAP XIV 
rienced and an ideal tzrminable annuity of the same present 
value. A government has to meet a series of expenses 
connected with its bonded debt. These expenses constitute, 
Jet us say, a stream of outgo lasting ten years, and consisting 
of nine equal payments —nominally “interest’’—and one 
much larger payment, exceeding the others by the amount 
of the so-called “principal.” T he sinking fund is merely a 
device for equalizing all ten payments. If the actual pay- 
ments are $5000 a year for nine years and $105,000 in the 
tenth year (as is the case of 10-year “five per cent’’ bonds), 
the ideal 10-year annuity equivalent to this series would, 
on a 4 per cent basis, be $13,329. The government, there- 
fore, if it would pay off its debt, or rather provide for it in 
ten equal installments, must during each of the first nine 
years, besides paying the $5000 to its creditors, pay into 
the sinking fund $8329. In the tenth year the process is 
reversed, and the entire $100,000 then accumulated in the 
sinking fund is taken to pay the $100,000 of “principal.” 
Hence, as applied to bonded debts, the sinking fund may be 
defined as formed by accumulating an annual sum during 
a, specified period, such that its amount will just suffice 
to extinguish a given sum at the end of that period. 
§8 
Depreciation and sinking funds are not the only devices 
by which uneven income streams may be, as it were, 
smoothed out. Many other devices may be employed. For 
instance, a person engaging in an unusual expense, such as 
that of building a house, will not allow this expense to 
seriously interrupt the even flow of his income, but will 
provide for it by some correspondingly unusual item of in- 
come. He may sell other property, for instance railway 
shares; the unusual sum he realizes on the sale will then 
offset the unusual outgo for the dwelling. Or, he may 
mortgage his dwelling and the land on which it stands, 
and pay the debt off gradually —sell a claim upon the