The foregoing shows many interesting changes in the comparative shipments, but needs no further explanation. The Treasury Department has compiled an interesting statement exhibiting the value of merchandise, whether of domestic or foreign produce, exported, and of foreign merchandise imported into the six principal collection districts of the United States, to wit:-Boston, New York, Philadelphia, Baltimore, New Orleans, and San Francisco, during the quarters ending September 30 and December 31, 1856, and March 31, 1857.

In the first quarter, the aggregate value, in the six districts, of exported domestic produce amounted to $53,594,770; of exported foreign merchandise, $3,197,771; and imported foreign merchandise, $89,730,323—making a total of $146,522,864 for exports and imports.

In the second quarter, the aggregate exports of home produce amounted to $69,118,123; exported foreign merchandise, $2,936,395; and the imports, $64,181,703—making a total of $136,236,221.

In the third quarter, the aggregate exports of home produce were $69,648,285; exported foreign produce, $6,536,316; and imports, $92,510,924-showing a total of $168,995,525. Thus in the three quarters, and for the six principal collection districts, the statistics show

Exports of domestic produce...

Exports of foreign produce...

Imports...

Total value of exports and imports for 9 months, ending March
31, 1857.....

$192,661,178 12,670,482 246,422,950

$451,754,610

These imports and exports were divided among the six districts specified as follows:

FOR NINE MONTHS ENDING MARCH 31, 1857.

Of the $12,670,482 worth of foreign merchandise exported during the three quarters, $7,323,072 were free, and $5,347,410 dutiable. Of the imported foreign merchandise amounting to $246,422,950, there was $24,158,187 free, and $212,264,767 dutiable.

The totals above given would show a balance in favor of the imports of over forty million dollars, but the summary for the six collection districts does not give the warrant for striking any such balance of our foreign commerce. There are in the United States eighty collection districts. At the six which were indicated in the official summary, the excess of imports over exports is about forty million dollars, even after including the shipments of specie; but the footings at the remaining seventy-four districts will make a very different showing, as at most of them the exports far exceeded the imports. This is easily illustrated by a comparison of the result for the last fiscal year :—

The above shows that while the imports for "the six districts," for the last fiscal year, were $44,287,134 in excess of the exports, the total for the whole country was twelve million less than the exports. If it be desirable to show the balance of trade, for the whole country, for the three quarters ending March 31st, the addition to the official returns from the six districts, of three-fourths the imports and exports of the remaining seventy-four districts for the last year, will give a nearer approximation to the truth :—

The above would be the relative totals for the nine months ending March 31st, provided the seventy-four districts stood this year as last; but it is well-known that, although there is some decline in the cotton shipments, the exports from many of the smaller ports largely increased during the early part of the current year, and in a far greater ratio than the imports. The "six ports" are Boston, New York, Philadelphia, Baltimore, New Orleans, and San Francisco. The remaining seventy-four districts can be copied from any official record. The principal are Charleston, Savannah, Mobile, Richmond, Oswego, and Champlain, but including all other lake, Atlantic, gulf, and Pacific ports.

NEW YORK COTTON MARKET FOR THE MONTH ENDING JUNE 19, 1857. PREPARED FOR THE MERCHANTS' MAGAZINE BY CHARLES W. FREDERICKSON, BROKER, NEW YORK.

Since the date of my last monthly report (May 22) no new feature of importance has occurred, to vary the almost monotonous state in which our market has existed during the past four weeks. The demand has been extremely moderate, either for export, speculation, or the home trade. The foreign advices have not been of a character to induce shipments to any extent, and most of that which has gone forward has been under advances, or in pursuance to Southern orders. For speculation, the season may be said to be over; while the demand for the home trade has been lessened by their continued orders being executed in the Southern ports, and perhaps a larger quantity of cotton has been ordered this year direct than ever before for home consumption. Prices have varied but slightly during the past month, and the total sales are estimated at 34,000 bales, inclusive of parcels in transitu. Stock on hand and on shipboard is counted at 60.000 bales, a large portion being low grades.

The sales for the week ending May 29th were 8,000 bales, the market resting in favor of holders, who offered their stocks sparingly. The sales were mostly for export, the home trade declining to meet the exactions of sellers. The market closed firm at the following:

PRICES ADOPTED MAY 29TH FOR THE FOLLOWING QUALITIES:

For the week ensuing there was less inquiry, and prices were a shade easier on sales of about 6,000 bales. Although the foreign advices were heavy, there was no pressing for sale, and the market closed quiet at the annexed rates:

PRICES ADOPTED JUNE 5TH FOR THE FOLLOWING QUALITIES:

Holders continued firm during the week ending June 12th, and the transactions were limited to the wants of the home trade until the close of the week, when, under favorably construed foreign advices, the sales were large. The total transactions for the week were 11,000 bales, the market closing steady at the annexed :

PRICES ADOPTED JUNE 12TH FOR THE FOLLOWING QUALITIES:

For the week ending at date the transactions were estimated at 9,000 bales, one-third being in transitu. The firmness of holders, and the small quantity on sale, restricted operations, and the market closed with much steadiness at the annexed rates:

PRICES ADOPTED JUNE 19TH FOR THE FOLLOWING QUALITIES:

The growing crop is represented as three to four weeks late, but the increased breadth of land planted may offset the backwardness of the season, and produce a large crop.

JOURNAL OF BANKING, CURRENCY, AND FINANCE.

WHAT RATE OF INTEREST DO OUR BANKS CHARGE ON THEIR DISCOUNTS? FREEMAN HUNT, Esq., Editor of the Merchants' Magazine, etc :—

SIR-It has doubtless occurred to all who have had dealings with our banks, that their method of computing interest on the face of a note, instead of on the sum loaned, requires the borrower to pay more than the nominal rate of interest on the amount he receives; but perhaps all have not attentively considered the large aggregate of profit which thus accrues to the banks.

It is said that some eminent lawyers have been of the opinion that this method of computation is defensible at law; but if there is any law by which it can be sustained, such an enactment would appear to be inconsistent with the statute limiting the rate of interest to seven per cent; and furthermore, mathematical analysis, to which such questions would seem to belong, will not support such an opinion. We propose to show this very briefly.

The true present value of a bill maturing at a future date, is a sum which, if put at interest, will amount to the face of the bill at its maturity. Suppose p to represent this value, a the amount or face of the bill, t the time, r the nominal, and R the true rate of interest, d the true discount, and b the discount accruing to bank custom; then, as d is the interest on the true present value, we have

which gives the excess of the true over the nominal rate; therefore for the true rate we have

When r is a constant quantity, this value of R varies as t—that is, the longer the time the greater the rate, and conversely,

that is, on a note of 90 days the borrower pays about 7 per cent on the sum he receives instead of 7 per cent, and discounting by this method for one year, he would pay 7 per cent.

As an illustration of what has been written, let us assume that the loans by the banks of this city, during the present year, will amount to $600,000,000, and at an average time of 60 days. Let S represent this sum, then we have

which is the amount the banks would loan did they compute discount on the sum loaned instead of on the face of the paper discounted-from which we find that the sum paid to the banks, over the nominal rate of interest, would be $79,450. Convenient formula for the computation of the true present value and true discount are readily deduced from a preceding equation, thus—

t being expressed in years and decimal parts of a year. Example: what is the true present value of a note for $10,000, maturing in 73 days at 7 per cent? By formula, (4.)

Example:-If the bank discount on a 3 month's bill amounts to $350, what is the true discount?

By formula, (5.)

In a former article, published in the May number of this Magazine, the equation on page 591

y

should read,

Ꭹ

"Old Rapid" must have read "Methods of Computing Interest," published in your issue for May, with singular and fatal rapidity, to have so completely mistaken the scope of that article as is indicated by a note from him, which I find