Elementary arithmetic, with brief notices of its history... by Robert Potts.

7
The compound interest of any sum can be found by a shorter
process, by simply taking the same aliquot parts of the principal of
each successive year, as the rate per cent. is of ~100.
6. Discount is defined to be a deduction made for the present payment of a sum of money due at some future time, and differs from
simple interest or Banker's discount.
If ~100 be lent for one at 5 per cent. per annum, the amount at
the end of the year would be ~105.
But if ~100 be due at the end of a year at the rate of 5 per cent.
interest per annum, and if ~5 be deducted for present payment, the
sun paid to the creditor would be ~95.
Now if this ~95 were put out immediately to interest for a year,
at 5 per cent.; at the end of the year the amount would be ~99. 15s.;
whereas if the payment had been deferred till the end of the year, the
creditor would have received ~100, and would not have lost 5s.; in the
transaction he should have lost nothing.
It is therefore clear that ~5 was too large a sum to be deducted
for present payment. The interest should have been calculated on
the present worth of ~100, and not on the worth of ~100 at the ecnd of the
year.
And since the present worth of ~105 due at the end of a year is ~ 100,
the present worth of ~100 due at the end of a year will be a fourth proportional to ~105, ~100, ~100, which will be found to be ~95. 4s. 9dc.,
and the difference ~4 15s. 2-d., between this present worth of ~100,
and ~100 due at the end of the year, is the interest of the present
worth for the same time and at the same rate of interest. The interest of
the present worth is also a fourth proportional to ~105, ~100, ~5;
which will be found to be ~4. 15s. 2-d.
By means of these principles, may be found the tine at which one
payment may be made equal to the sum of several payments made at
different times, at the same rate, or at different rates of interest. If
the present worth of the different sums be found separately for the
times and at the rates of interest given, then the time may be found
when the sum of the present worths shall be equitably equivalent to
the amount of the given sums at the given rate of interest.
It may be added that the present worth and the discount of any
sum due any number of years hence, may also be calculated by compound interest by means of a proportion.
7. The purchase and sale of stocks, whether they consist of the
national debts of governments, or the nominal capital of trading colmpanies, are all subject to the rule of proportion, as well as all questions
which arise on the dividends of such stocks. The national debts of
foreign governments in general consist of bonds of ~100, or some
multiple or submultiple of that sum. They are contracted for a fixed
rate of annual interest payable half-yearly, and are so arranged as to be
gradually paid off within a certain number of years. They are trans