Note 101 — PART II. CONTAINING Remarks on some Particulars in a Speech at opening the Budget in April 1776.

There is another very great advantage which would attend these annuities.—One and the same surplus would discharge a given capital in less time. For example. A surplus of a million per ann. invariably applied, and the first payment to be made immediately, would discharge a capital of a hundred millions bearing 3 per cent. interest in 46 years. But if the same capital bore 3½ per cent. interest, it would be discharged in 43½ years; if 4 per cent. in 40 years; if 5 per cent. in 37¼ years.—A capital less than a 100 millions, in the same proportion that the interest is more than 3 per cent. and for which, therefore, the same annuity is paid, (as in the present case) the same surplus would discharge in 39 years, if the interest is 3½; in 34¼ years, if the interest is 4 per cent. in 27¼ years if the interest is 5 per cent.—Supposing, therefore, 75 millions borrowed in the manner of our Government, by creating a capital of a 100 millions bearing 3 per cent. (that is, by selling 3 per cent. stock for 75l. in money) which might have been borrowed by creating a capital of only 75 millions bearing 4 per cent. (that is by selling 4 per cent. stock at 100) there will not only be a loss of 25 millions by a needless increase of the capital; but also a loss of 14 millions, by an increase of the time in which one and the same saving will discharge the two capitals.—This may be proved in the following manner.—A million, per ann. will, in 34 years and a quarter, very nearly discharge a debt of 75 millions bearing interest at 4 per cent.; but the same saving will, in the same time, discharge only a capital of 61 millions, if it bears interest at 3 per cent. When, therefore, such a saving has compleated the redemption of the one capital, there will remain unpaid of the other, 39 millions.—What has been now applied to a large sum holds true in proportion of any smaller sums.

It appears from hence to be a very wrong observation which some have made; “that provided the annual charge is the same, it signifies little what the principal of the public debt is.”—As there is no way of removing the annual charge but by paying the principal, it is of just as much consequence what it is, as whether it is practicable or impracticable, to remove a burden which weakens and cripples, and must in time sink the public. An annuity of Six Millions, if the principal is Hundred Millions borrowed at 6 per cent. might be redeemed in 33 years with a million per ann. surplus. But if the principal is Two Hundred Millions bearing 3 per cent. the same surplus would, in the same time, pay off only 56 millions; and but little more than a quarter of the annuity would be redeemed. If, therefore, the same sum might as well have been obtained by creating a principal of a hundred millions bearing 6 per cent. as by creating a capital of two hundred millions bearing 3 per cent. there will be a needless expence, in discharging the debt, of 144 millions.