Note 58 — 1769.

Upon the money borrowed in 1760, the premium of one per cent was for twenty-one years, not for twenty; this annuity has been paid eight years instead of seven; the sum paid is therefore 640,000l. instead of 560,000l.; the remaining term is worth, ten years and a quarter instead of eleven years;[59] its value is 820,000l. instead of 880,000l.; and the whole value of that premium is 1,460,000l. instead of 1,440,000l. The like errors are observable in his computation on the additional capital of three per cent on the loan of that year. In like manner, on the loan of 1762, the author computes on five years' payment instead of six; and says in express terms, that take 5 from 19, and there remain 13. These are not errors of the pen or the press; the several computations pursued in this part of the work with great diligence and earnestness prove them errors upon much deliberation. Thus the premiums in 1759 are cast up 90,000l. too little, an error in the first rule of arithmetic. "The annuities borrowed in 1756 and 1758 are," says he, "to continue till redeemed by Parliament." He does not take notice that the first are irredeemable till February, 1771, the other till July, 1782. In this the amount of the premiums is computed on the time which they have run. Weakly and ignorantly; for he might have added to this, and strengthened his argument, such as it is, by charging also the value of the additional one per cent from the day on which he wrote, to at least that day on which these annuities become redeemable. To make ample amends, however, he has added to the premiums of 15 per cent in 1759, and three per cent in 1760, the annuity paid for them since their commencement; the fallacy of which is manifest; for the premiums in these cases can he neither more nor less than the additional capital for which the public stands engaged, and is just the same whether five or five hundred years' annuity has been paid for it. In private life, no man persuades himself that he has borrowed 200l. because he happens to have paid twenty years' interest on a loan of 100l.