px + qx + rx + sx + tx= q X BC + r X BD + s X BE + t X BF (p + q + r + s + t) x = x q X BC + r X BD + s X BE + t x BF. p + q + r + s + t. Hence the following general rule: multiply the several payments to be made by the respective times from the first payment, add them together and divide that sum by the whole amount of the bills for the time sought, which is to be counted from the time on which the first payment falls due. SOLUTION OF QUESTION I. CASE I. 334 1st March x 19th July. 10th April. 1st Ap. Let x = average time from 1st April, then 1500 x + 250 (x—9) + 643 (x-109) = 1400 (334 — x) then 1500 x + 250 x -- 2250 + 643 x - 70087 = 467600 - - 1400 x. Again, 1500 x + 250 x + 643 x + 1400 x = 467600 + 70087 2250 + 70087 + 467600 + 2250 and x= = 142 days 3793 after the 1st day of April, which agrees with the 21st day of August, 1840, as before. SOLUTION OF CASE I. BY ANOTHER PRACTICAL METHOD. It of the first bill is $150 X 0 000 2d 25 x 9 225 64 109 6976 4th 140 x 334 = 46760 3d 379 379)53961(142 Note.--Agreeably to mercantile usage, a fraction less than one-half in dollars or days is omitted in the equation of payments, and when more than a half, it is considered as a unit. CASE II. 1. Sold merchandise at different times, and on various terms of credit. 1839 September 6th $100 for 1 month, due Oct. 6th. 14th 14th. Dec. 10th. November 14th 340 6 3 66 Feb. 14th. June 14th. days. 8 125 X 1196 1196)171371(= 144 + 144 days from the 6th October will come to February 27, 1840, at which time a note for $1196 would be due. SECOND METHOD. 14th 125 x 243 14th 340 x 120 June 14th 456 X 000 1196)128825(= 108 + $1196 Due by average 108 days earlier than the 14th day of June 1840, which will be the 27th day of Feb. as above. THIRD METHOD. 1839 September 6th $100 x 30 14th 38 October 10th 95 November 14th 340 X 161 January 14th 456 x 281 125 X 175 X 1196 1196)207251(174 + 174 days from the 6th September, which will make the average time fall on the 27th day of Feb. 1840, as before. AVERAGE CALCULATIONS BY INTEREST. days. 14th 125 X 38 1196 Interest, $34.57 As $11.96 : 60 : : $34.57 = 174 days, nearly being the time required for $1196 to gain $34.57, the whole time by equation from the 6th Sept. to the 27th February. CASE III. To average personal accounts when goods are received in barter. Rule.-Find the average time for the debtor and creditor sides of the accounts, and multiply the least sum by the difference of time, divide the product by the difference of the accounts, and the quotient will be the number of days to be carried forward. Illustration.-Sold Barton & Co. Philadelphia, merchandise at different dates and credits for $600 due by average 6th September. Received from Barton & Co. at different times, goods amounting to $1000, due by average on the 6th January, 1841, required the time of payment for the balance due the firm? From $1000 Least sum $600. Take 600 400 Difference of time from 6th September to 6th January. 600 x 91 400)546(00 1364 days. Due by average 1363 days from the 6th day of January, which falls due on the 23d day of May. From the 6th September to the 23d May (average time) is 227) days, and 600 x 227} = 1000 x 1363 = 1860546 $22.75 equated interest for Dr. and Cr. CASE Y. ANOTHER METHOD. 1. A. B. purchased merchandise on credit at different times, and is desirous to pay the whole amount at a certain period, required the time by equation? Sales made as per bill rendered. dolls. days. product. 1840 May 4th $52.00 X 4 8th 13.87 66 x 29 June 6th 104.20 170 X 4 10th 84.16 254 x 34 July 14th 125.04 000 x 0 379)11438(30 Thirty days counted back from July 14th will give the equated time on the 14th of June. EXCHANGE. Q. What is Exchange? A. It is the paying or receiving money in one country, for its equivalent in the money of another country by means of Bills of Exchange. Q. What is meant by a Bill of Exchange? A. A Bill of Exchange is a written order for the payment of money at an appointed time. Q. Who is the drawer? A. The person to whom the bill is addressed, is called the acceptor; when he engages, to pay the bill. Q. What is meant by endorsing a Bill? A. When the holder of a bill, disposes of it, he writes his name on the back, which is called endorsing. Q. Are there other persons occasionally concerned in a Bill of Exchanger A. Yes, the buyer or remitter, the seller or negociator, and the holder or possessor. Q. Who should be the first endorser to a Bill? A. The payee. Q. What is a draft called, when a Merchant in the U. S. draws on his Banker in London? A. "Bill on London,” and vice-versa. 18* |