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time, to be counted from the earliest date of any sum in the account becoming due, FORWARD when the larger sum of products is on the LARGER side of the account, but BACKWARD when it is on the SMALLER side.

Note. — The CASH VALUE of a balance of an account drawing interest, or whose items are on different terms of credit, depends upon the time of settlement, and is therefore either larger or smaller than the difference between the debit and credit items.

The average time of a balance becoming due being known, its cash value may be found, when the balance is due BEFORE the time of settlement, by adding to the balance interest up to the time of settlement; and when due AFTER that time, by deducting from the balance interest for the time intervening between the time of settlement and the time of the balance becoming due. The deduction of interest, in the latter case, is the mercantile method, instead of that of finding the true present worth by deducting the true discount.

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EXAMPLES.

2. Required the time when the balance of the following accounts becomes subject to interest, allowing that each item was due from its date. Dr. D. Wadsworth in account with S. Adams.

Cr.

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3. When did the balance of the following account become due, the merchandise items being on 6 months ? Dr. John Greene in account with F. Johnson.

Cr. 1856.

1856. March 1, To merchandise, $ 720.75 April 1, By cash,

$ 700.00 20,

815.30 May 30,
* merchandise,

569.89 April 11, 587.80 July 20,

500.00 30,

300.00
Sept. 25,

100.00 June 15,

625.25
30, merchandise,

750.20 July 18, 560.00 Oct. 30,

329.96 Aug. 30,

684.90
Nov. 20,

500.00 Sept. 25,

365.30

cash,

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4. Allowing that each item of the following account draws interest from its date, at what time would the balance become due, and how much ready money should in equity discharge the same, September 21, 1856, interest being at 6

per cent. ?

Dr.

I. Bradley in account with T. B. Fuller.

Cr.

66

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1856.

1856. March 1, To merchandise, $36.25 April 1, By cash, $ 48.25 April 7, 18.15 May 20,

90.10 June 15,

48.26
June 17,

12.50 July 21,

91.20
July 4,

20.00 Aug. 1,

30.00
10,

25.00 Ans. November 21, 1856; cash value of balance, $ 27.73.

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5. Required the time when the balance of the following account became subject to interest, allowing the merchandise to have been on 8 months; and the cash value of the balance on November 28,1857, provided it drew 6 per cent. interest from the time of its becoming due. Dr. N. Chandler, 2d, in account with T. E. Lanman. Cr.

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u cash, • draft,

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1856.

1857. May 1, To merchandise, $ 300.00 Jan. 1, By cash,

$ 500.00 July 7,

759.96 Feb. 18,

« merchandise, 481.75 Sept. 11, 417.20 Mar. 19,

750.25 Nov. 25, 287.70 April 1,

210.00 Dec. 20, 51.10 May 25, cash,

100.00 Ans. July 28,1857; cash value of balance, $ 299.88. 6. The following account was settled May 24, 1857; how long previous to date was the balance by average due, and what was the cash value of the balance at the time of settlement? Dr.

David Taggart in account with George Perry. Cr. 1856.

1856. Jan. 1, To m'dise on 5mo., $ 560.00 March 7, By m'dise on 6mo., $ 350.00 Feb. 11, on 6io., 846.00|| April 17,

820.00 Mar. 20,“ on 6mo., 728.00 June 20,

cash,

100.00 July 30, “ cash, 400.00|| Aug. 15,

800.00 Sept. 12, m'dise on ômo., 560.00 Sept. 18, " m'dise on 6mo., 630.00 Dec. 18, 600.00 Oct. 28,

400.00 1857.

Nov. 1,

m'dise on 4mo., 750.00 May 10,1

500.00 Ans. May 19, 1856; cash value of balance, $ 364.93.

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439.° To find the true balance of an account current whose items draw interest.

Ex. 1. Required the true balance of the following account, on November 1, 1857, the time of settlement, allowing that each item drew interest from its date, at the rate of 6 per cent.

Ans. $ 430.04.

Dr.

Wesley Scott in account with Seth Wilson.

Cr.

66

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July 4,

1857.

1857. Jan. 17, To merchandise, $ 144.05 Feb. 1, By cash,

$ 200.00 Mar. 20, 374.95 March 9,

300.00 May 7, 500.00 | April 1,

600.00 100.00 5, “ merchandise,

180.00 7, merchandise, 600.00 | June 12. 4

700.00 Sept. 25, 250.00 Aug. 19, cash,

400.00 Nov. 1,] “ *bal. new acc't, 430.04 Nov. 1 66 *balance of int., 19.04 1$ 2399.04

$ 2399.04

* cash,

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Errors excepted.

Philadelphia, November 1, 1857.

SETH WILSON.

4 May 66 July

OPERATION.
Debits.

Credits.
Due Jan. 17, 144 X 288 41472 Due Feb. 1, 200 X 273 54600
March 20, 375 X 226 84750

March 9, 300 X 237 71100 7, 500 X 178 89000.

April 1, 600 X 214 128400 4, 100 X 120 12000

5, 180 X 210 = 37800 7, 600 X 117 70200

June 12, 700 X 142 = 99400 Sept. 25, 250 X 37 9250

Aug. 19, 400 x

74 =

29600 $ 1969 6) 306.672

$ 2380 6 ) 420.900 $ 51.112

$ 70.150 $ 2380 - $ 1969 $ 411, balance of items. $ 70.15 $ 51.11 = $ 19.04, balance of interest. $411 + $ 19.04 $ 430.04, true balance.

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The time in days intervening between the date of each item and the time of settlement is, evidently, the number of days each item is on interest. Then, if each item be multiplied by the number denoting its number of days, and divided by 6000, the result will be its interest (Art. 356, Note 1), and the sum of the interest of the several items of debit will be the aggregate interest of the debit side, and the same principle will hold in finding the aggregate interest of the credit side. But the same result may be obtained in a shorter way by dividing the sums of the debit and credit products by 6000, which is done most readily by pointing off three decimal places at the right of each sum (Art. 78), and dividing by 6, as in the operation. Then the balance of items and the balance of interest we add together, and thus obtain the true balance.

2. Required the true balance of the following account, on October 1, 1857, the time of settlement, allowing the rate of interest to be 6 per cent.

Ans. $ 189.81.

* Introduced only to illustrate the manner of balancing the account.

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Dr. Grant & Barker in account and interest with J. Ritchie. Cr. 1857.

1857. Mar. 1, To balance of old acc't, $ 100.15 Mar. 15, By m’dise on 6mo., $ 160.00 15, “ cash paid draft, 40.00 April 1, cash,

100.00 Mar. 20, “ merch'dise on 6mo., 180.85 June 1, draft,

120.00 Oct. 1, " *balance,

189.81 Aug. 10,

m'dise on 2mo., 80.00 Sept. 1, o cash paid draft, 50.00 Oct. 1, " * balance of int.,

.81

$ 510.81 $ 510 81

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Credit products.

Debits.
Due March 1, 100 X 214 =

15, 40 X 200
“ Sept. 20, 181 x 11 =

$ 321

OPERATIOX.
Debit products.

21400
8000
1991

31391

16 June

Credits.
Due April 1, 100 X 183

18300
1, 120 X 122

14640 " Sept. 1, 50 x 30

1500 15, 160 X 16

2560 16 Oct. 10, 80 X 9

720 $ 510

32111

37000 321

32111 189 balance of items.

6 ) 4.889

$ 0.81 bal. of interest. $ 189 + $ 0.81 $ 189.81, true balance.

We find the several products by multiplying, as in working the preceding example. The products belonging to items becoming due previous to settlement we arrange as belonging to their respective sides. One item, however, becomes due 9 days afier the time of settlement, thus requiring its side to be diminished by the interest of that item for the 9 days, or that the opposite side should be increased by that interest. We, therefore, write the product of this item with the debit products. We may now find the interest of each side separately, and then subtract that of the one side from that of the other for the balance of interest; but we obtain the desired result by a shorter method by finding the interest corresponding to the difference of the sums of the debit and credit products. Hence the general

RULE. — Multiply each item of debit and credit by the number of days intervening between its becoming due and the time of settlement.

Place the product of each item becoming due BEFORE the time of settlement on its own side of the account, and place the product of each item

* Introduced only to illustrate the manner of settlement.

becoming due AFTER the time of settlement on the side opposite to its

ост.

The difference of the sums of the debit and credit products, with three places pointed off on the right for decimals, divided by 6, will give the balance of interest.

Place the balance of interest on its own side of the account, and the difference then between the two sides will be the true balance.

Note 1.- - The interest as found by the rule is that at 6 per cent. From which the interest at any other rate may be found by aliquot parts.

NOTE 2. Besides the above method of settling accounts drawing interest, accountants often make use of tables constructed to aid in equating and balancing accounts.

EXAMPLES.

3. Alfred Hicks is in account and interest with Keen & Lee, as follows: Debtor, January 1, 1857, to merchandise, on 6 months, $ 156.10; February 3, to cash paid draft, $ 100; March 20, to merchandise, on 4 months, $ 316.90; March 30, to merchandise, on 4 months, $ 162.00; May 15, to cash paid draft, $ 100; August 20, to merchandise, on 6 months, $ 213.00. Creditor, February 1, by cash, $120.00; March 20, by merchandise, on 4 months, $ 420.16; May 1, by merchandise, on 6 months, $300; July 1, by merchandise, on 4 months, $ 50; September 10, by merchandise, on 4 months, $ 99.84. Required the true balance, if settled on December 1, 1857, interest being at 6 per cent.

Ans. $ 61.36. 4. Required the true balance due on the following account, on March 25, 1857, each item drawing 7 per cent. interest from its date. Benjamin Lyman in account and interest with John Russell: Debtor, July 4, 1856, to merchandise, $ 200; September 8, to merchandise, $ 300; September 25, to merchandise, $ 250 ; October 1, to merchandise, $ 600; November 20, to merchandise, $ 400; December 12, to merchandise, $ 500 ; January 15, 1857, to merchandise, $ 100; March 11, to merchandise, $ 120. Creditor, July 20, 1856, by cash, $ 300 ; August 15, by cash, $ 350 ; September 1, by cash, $ 400 ; November 1, by cash, $ 320; December 6, by merchandise, $ 600; December 20, by cash, $ 100; February 1, 1857, by cash, $ 200; February 28, by merchandise, $ 150.

Ans. $ 50.64.

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