APPENDIX TO CHAPTER XIV 401
entirely just if the impairment of one capital were always
offset by the equal increase of some other capital, z.e. if
the taxpayer's total capital-value were kept at the same level.
In general, large receipts are usually reinvested and should
therefore not be subject to the income tax at all. If we could
assume such reinvestment to be the invariable rule, we could
approve of the system by which, in England, a terminable an-
nuity is not taxed as income at its full value, but is taxed only
on that part of it which constitutes “interest.” The other part,
which constitutes impairment of principal, is not taxed. The
system, of course, fails of justice in cases where this impairment
of principal is never restored in some other form of investment
but ultimately represents, like the other part of the annuity,
through personal expenditure, final enjoyable income.
To illustrate the English exemption of impairment of capital,
if $1000 is paid for a five-year annuity on a basis of 4 % inter-
est (reckoned semi-annually), it will purchase an annuity of
$111.33 at the end of each six months, and the following will
be the schedule showing the capital-value at each interval, the
interest accruing upon it, the payment to the beneficiary, and
the impairment of capital resulting.
CAPITAL | INTEREST ToraLn IMPAIR- | CAPITAL
AT BEGIN-| ACCRUED | PAYMENTS | MENT OF | LEFT AT
NING AT END AT END | CAPITAL Exp
1st half year . . . . [$1000.00 $20.00 [$111.33 $91.33) $908.67
2dhalf year :. ......x 908.67 18.17 111.33 93.15] 815.52
8d hall-year . . . . 815.52] 16.31 111.33 95.02] 720.50
4th balf year , . . . 720.50] 14.41 111.33 96.92 623.59
Sth haf year’. . . . 623.59) 12.47 111.33 98.86] 524.73
6th half year . . . . 524.73] 10.50 111.33 100.83] 423.90
Th half year “2 Wn 423.90 8.48 111.33 102.85) 321.05
8th half year . . . . 321.05 6.42 111.33 104.91] 216.15
Othohalf year... ... ..iis 216.15] 4.32 111.33 107.00] 109.14
10th hall year . . . 109.14) 2.18 111.33 109.14] 000.00
$1000.00
If at the start he has a capital of $1000, at the end of the
1 From Institute of Actuaries’ Text-book, Part I, “Interest,” by Ralph
Todhunter, p. 57. London (Layton), 1901.
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