Sec. 11] VALUE OF CAPITAL 225

still be regarded as the discounted value of an income
which is indefinitely postponed, but indefinitely great. Of
course, such a limiting case is of purely theoretical interest.
The prodigious sums which result from the reckoning of
compound interest always surprise those who have never
made such computations. One dollar put at compound
interest at 4 per cent would amount, in one century, to
$50, in a second century to $2500, in a third century
to $125,000, in a fourth century to $6,500,000, in a
fifth century to $325,000,000, and in a sixth century to
$16,000,000,000. Beyond this the figures are almost
unthinkable in magnitude.'
Yet we have few instances in which any one has endeavored
 to set aside even one dollar for the benefit of posterity
six centuries removed! There is too much reluctance to
build for the remote future, even though the attainable
results are enormous. Benjamin Franklin, at his death
in 1790, left £1000 to the town of Boston and the same sum
to Philadelphia, with the proviso that it should accumulate
for a hundred years, at the end of which time he calculated
that at 5 per cent it would amount to £131,000. In the
case of the Boston gift, it actually amounted, at the end
of the century, to $400,000, and has since accumulated to
about $600,000. The sum received by the city of Philadelphia
 has not increased nearly as fast.
Another interesting case of accumulation is that of the
Lowell Institute in Boston, which was founded by a bequest
of $200,000 in 1838, with the condition that 10 per cent of
the income from it should be reinvested and added to the
principal. The peculiarity of this provision is that it
applies in perpetuity. There is, therefore, theoretically no
limit to the future accumulation thus made possible.
The fund, after sixty-seven years, amounts already to
$1,100,000.
It must be remembered however that practically even a
1 For a geometrical representation, see Appendix to Chap. XIII, § 16.
Q