It maybe satisfactory to see stated in figures the yearly progression of reimbursement of the million of dollars, and their interest at 7½ per cent. effected by the regular payment of —— dollars annually. It will be as follows:
| Borrowed, $1,000,000. | |||||||
| Balance after | 1st | payment, | $975,000 | Balance after | 11th | paym't, | $594,800 |
| " | 2d | " | 948,125 | " | 12th | " | 539,410 |
| " | 3d | " | 919,234 | " | 13th | " | 479,866 |
| " | 4th | " | 888,177 | " | 14th | " | 415,850 |
| " | 5th | " | 854,790 | " | 15th | " | 347,039 |
| " | 6th | " | 818,900 | " | 16th | " | 273,068 |
| " | 7th | " | 780,318 | " | 17th | " | 193,548 |
| " | 8th | " | 738,841 | " | 18th | " | 108,064 |
| " | 9th | " | 694,254 | " | 19th | " | 16,169 |
| " | 10th | " | 646,324 | ||||
If we are curious to know the effect of the same annual sum on loans at lower rates of interest, the following process will give it:
From the Logarithm of a, subtract the Logarithm r-i, and from the number of the remaining Logarithm subtract s, then subtract the Logarithm of this last remainder from the difference between the Logarithm a and Logarithm r-i as found before, divide the remainder by Logarithm r, the quotient will be t. It will be found that —— dollars will reimburse a million,
| Years. | Dollars. | |||||
| At 7½ | per cent. | interest in | 19.17, | costing | in the whole | 1,917,000 |
| 7 | " | " | 17.82, | " | " | 1,782,000 |
| 6½ | " | " | 16.67, | " | " | 1,667,000 |
| 6 | " | " | 15.72, | " | " | 1,572,000 |
| 5½ | " | " | 14.91, | " | " | 1,491,000 |
| 5 | " | " | 14. 2, | " | " | 1,420,000 |
| 0 | " | " | 10. | " | " | 1,000,000 |
By comparing the 1st and the last of these articles, we see that if the United States were in possession of the circulating medium, as they ought to be, they could redeem what they could borrow from that, dollar for dollar, and in ten annual instalments; whereas, the usurpation of that fund by bank paper, obliging them to borrow elsewhere at 7½ per cent., two dollars are required to reimburse one. So that it is literally true that the toleration of banks of paper-discount, costs the United States one-half their war taxes; or, in other words, doubles the expenses of every war. Now think, but for a moment, what a change of condition that would be, which should save half our war expenses, require but half the taxes, and enthral us in debt but half the time.
Two loans having been authorized, of sixteen and seven and a half millions, they will require for their due reimbursement two millions three hundred and fifty thousand dollars of the three millions expected from the taxes lately imposed. When the produce shall be known of the several items of these taxes, such of them as will make up this sum should be selected, appropriated, and pledged for the reimbursement of these loans. The balance of six hundred and fifty thousand dollars, will be a provision for 6½ millions of the loan of the next year; and in all future loans, I would consider it as a rule never to be departed from, to lay a tax of 1/10, and pledge it for the reimbursement.
In the preceding calculations no account is taken of the increasing population of the United States, which we know to be in a compound ratio of more than 3 per cent. per annum; nor of the increase of wealth, proved to be in a higher ratio by the increasing productiveness of the imports on consumption. We shall be safe therefore in considering every tax as growing at the rate of 3 per cent. compound ratio annually. I say every tax, for as to those on consumption the fact is known; and the same growth will be found in the value of real estate, if valued annually; or, which would be better, 3 per cent. might be assumed by the law as the average increase, and an addition of 1/33 of the tax paid the preceding year, be annually called for. Supposing then a tax laid which would bring in $100,000 at the time it is laid, and that it increases annually at the rate of 3 per cent. compound, its important effect may be seen in the following statement:
| The 1st | year | 103,090, | and reduces | the | million to | $972,000 |
| 2d | " | 106,090, | " | " | " | 938,810 |
| 3d | " | 109,273, | " | " | " | 899,947 |
| 4th | " | 112,556, | " | " | " | 854,896 |
| 5th | " | 115,920, | " | " | " | 803,053 |
| 6th | " | 119,410, | " | " | " | 743,915 |
| 7th | " | 122,990, | " | " | " | 676,719 |
| 8th | " | 126,680, | " | " | " | 600,793 |
| 915,913 |
| It yields the | 9th | year | $130,470, | and reduces | it to | $515,382 |
| 10th | " | 134,390, | " | " | 419,646 | |
| 11th | " | 138,420, | " | " | 312,699 | |
| 12th | " | 142,580, | " | " | 193,517 | |
| 13th | " | 146,850, | " | " | 61,181 | |
| 14th | " | 151,260 | over pays, | 85,491 | ||
| 1,759,883 |