Now, if we suppose these life-annuities worth 20 years purchase[26], this was the same thing as if government had given a deduction of 90_l._ out of the 400_l._ subscribed; consequently the remainder, which was 310_l._ produced 12_l._ This makes the rate of interest upon the loan to have been 3.87 _per cent._ And as government inclined that the loan should be made in that way, the lenders were willing that it should be so; and the difference between 3.87 _per cent._ (the then rate of money) and 4⅛ interest, which was paid by government, was a sinking fund, as it were, for the gradual extinction of the capital of the lottery for 500,000_l._ during the lives of the annuitants. In 1746, perpetual or indeterminate annuities were constituted at 4 _per cent._ and the premium upon the ten lottery tickets was raised to 9_l._ life-annuity. It would be unnecessary to trace the various methods of contriving the premiums given in the succeeding years of this war. The principle upon which they were regulated was always to proportion them to the rate of interest at the time; and the motive was, I suppose, that by this method of borrowing, a part at least of the debt would become extinguished with the lives of the subscribers. There might perhaps be another, to wit, that by swelling the capital, for value not received, there was an appearance of borrowing at a lower rate of interest than what in reality was the case. Thus in 1747, when 6 300 000_l._ were borrowed, instead of giving not quite 4½ _per cent._ for this sum, they gave 4 _per cent._ upon 6 930 000_l._ which capital, although money should return to 3 _per cent._ was still to stand at its full value; whereas, had 6 300 000_l._ been borrowed at 4½ _per cent._ there would have been a saving of 600 000_l._ upon the capital; and at the peace, the interest of 4½ _per cent._ would equally have come down to 3 _per cent._ with the other funds. Footnote 26: This may seem a high valuation, and is, in fact, far beyond what any of those annuities sold for: but as the interest of money cannot be estimated, for a constancy, at more than 3 _per cent._ and that probably the best lives were chosen, the value to government of such annuities may well be estimated at 20 years purchase. By De Moivre’s tables, annuities for the most favourable ages, interest being at 3 _per cent._ are valued at 19.87 years purchase; and his valuations are generally allowed not to be too high.