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EXAMPLES.

2. A merchant has $ 144 due him, to be paid in 7 months, but the debtor agrees to pay one half ready money, and two thirds of the remainder in 4 months. What time should be allowed for paying the balance ?

Ans. 2y. 10mo. 3. March 23, 1856, I sold John Morse goods to the amount of $ 8000 on a credit of 8 months. April 5, he paid me $1200; July 4, $ 1500 ; September 25, $ 1800 ; October 1, $ 1000; November 20, $ 500. When, in equity, should I receive the balance ?

4. There is due to a merchant $ 800, one sixth of which is to be paid in 2 months, one third in 3 months, and the remainder in 6 months; but the debtor agrees to pay one half down. How long may the debtor retain the other half so that neither party may sustain loss?

Ans. 8 months. 5. I have sold Charles Fox goods to the amount of $3051, on a credit of 6 months, from September 25, 1856. October 4, he paid $ 476; November 12, $ 375; December 5, $ 800; January 1, 1857, $ 200. When, in equity, ought I to receive the balance ?

Ans. October 8, 1857.

AVERAGING OF ACCOUNTS.

437. An Account Current is a statement of the mercantile transactions of one person with another, when immediate payments are not made.

An account is marked Dr. on the left, to indicate that the person with whom the account is kept is debtor for the items on that side; and is marked Cr. on the right, to indicate that he is creditor for the items on that side.

Accounts current are generally made up or settled at the end of every six months or year.

438. To find the equated time when the balance of an account current will be due.

Ex. 1. In the following account when did the balance be. come due, the merchandise articles being on 6 months' credit?

Ans. December 22, 1856.

Dr.

Messrs. James Dutton f. Co. in account with David Hale.

Cr.

$ 240.00

48.88 50.00 410.01

1856.

1856. Jan. 4. To merchandise, $ 96.51 Jan.30. By cash, 18.

57.67 Apr. 3. Feb. 4. “ cash paid draft, 80.00 May22.

46 merchandise, 38.96 July 7. “ Note, * June 22, 6mo. 9. cash paid draft, 50.26 Mar. 3. “ merchandise, 154.46 " 24.

42.30

23.60 May15.

28.46 21.

177.19

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Errors excepted. Settled as above, Boston, July 7, 1856.

David HALE,
By John Davis.

FIRST OPERATION.

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1856. Debits.

Credits. Due July 4, 97 X 151 - 14647 Due Jan. 30, 240 18, 58 X 165 9570

Apr. 3, 49x 64 = 3136
Feb. 4, 80

May 22, 50x 113 “ Aug. 4, 39 X 182 7098

$ 339

8786 days. Feb. 9, 50X 5 250

8786 = 339 Sept. 3, 154 X 212 32648

25397 days. 24, 42 X 233 9786

Credits due 26 days from January 30, Oct. 9, 24 X 248

5952

or on February 25, 1856. Nov. 15, 28 X 285 7980

Difference between February 25 and 21, 177 X 291 51507

August 8 = 165 days. $ 749 139438 days.

$ 749 - $ 339 = $ 410, balance. 139438 = 749 18644 days.

339 X 165 Debits due 186 days from February 4,

55935; or on August 8, 1856.

55935 : 410 1363 days. 136 days forward from August 8, 1856 December 22, 1856. On equating each side of the account (Art. 435), we find the debits became due 186 days from February 4, or on August 8; and the credits became due 26 days from January 30, or on February 25.

If the account had been settled on February 25, it is evident the debits would have been paid 165 days, or the time from February 25 to August 8, before having become due. This would have been a loss of interest to the debit side of the account, and a corresponding gain to the credit side. Now, as the settlement should be one of equity, we find how long it will take the balance, $ 410, to gain the same interest that $ 339 would gain in the 165 days. If it take $ 339 to gain a certain interest in 165 days, it would take $ 1 to gain the same interest 339 times 165 days 55935 days; and it would take $ 410 to gain the same amount of interest Ily of 55935 days 136

* Included only to illustrate the manner of settling an account.

days nearly. Hence, the balance became due 136 days forward from August 8, 1856, or on December 22, 1856.

The time was counted forward from the average date of the larger amount, since it became due last; but had that amount become due first, the time would have been counted backward from its average time.

SECOND OPERATION.

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9860

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9996

8786

Debits.

Credits.
Due Feb. 4, 80 X 5

Due Jan. 30, 240
9, 50 X 10 500 " April 3, 49 X 64 =3136
July 4, 97 X 156

“ May 22, 50 X 113 = 5650
18, 58 X 170

$ 339

8786 days. Aug. 4, 39 X 187 7293 “ Sept. 3, 154 x 217 33418 $ 749 $ 339 $ 410, balance of the 24, 42 X 238

items. Oct. 9, 24 X 253 6072 143183

134397, balance of “ Nov. 15, 28 X 290

8120 products. 21, 177 X 296 = 52392

134397 - 410 3279i7 days. $ 749 143183 days. 328 days forward from January 30, 1856 December 23, 1856. In the second operation, we take the earliest date on which any sum becomes due in the account, for the starting point from which to reckon the days, by which to find the several products belonging either to the debit or credit side (Art. 435, Note 1). The sum of the debit products, 143183, denotes the number of days required for $ 1 to gain as much interest as all the items of debit would gain in the times of their becoming due, and the sum of the credit products, 8786, denotes the number of days required for $ 1 to gain as much interest as all the items of credit would gain in the times of their becoming due. The difference between the sums of debit and credit products is 134397, and the difference between the debit and credit items is $410. Then, if it requires 134397 days for $1 to gain a certain interest, it will require $ 410 to gain the same amount 17 of 134397 days = 328 days nearly. 328 days forward from January 30, 1856 December 23, 1856, the time of the balance of the account becoming due; thus varying one day in the result, on account of the fractions.

RULE 1. Find the average time of each side becoming due.

Multiply the amount of the smaller side by the number of days between the two average dates, and divide the product by the balance of the acfount.

The quotient will be the time of the balance becoming due, counted from the average date of the larger side, FORWARD when the amount of that side becomes due LAST, but BACKWARD when it becomes due FIRST. Or, RULE 2. —

Multiply each sum of debit and credit by the number of days intervening between the date of its becoming due, and the earliest date on which any sum in the account becomes due.

Then, the difference between the sums of debit and credit products, divided by the difference between the debit and credit item, will give the

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.

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. 1855.

1855. July 4, To balance, $ 375.90

Aug. 10, By cash, $ 316.00 Aug. 20, " merchandise,

815.58
Sept. 1,

675.00 29,

178.25

25, “ merchandise, 512.25 Sept. 25, 387.20

161.75 Dec. 5,

418.70
Dec. 1,

100.00 Ans. August 6, 1855.

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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, Bv cash,

$ 700.00 20,

815.30 May 30, “ merchandise, 569.89 April 11, 587.80 July 20, cash,

500.00 30,

300.00
Sept. 25,

100.00 June 15,

625 25

“ merchandise, 750.20 July 18, 560.00 Oct. 30,

329 96 Aug. 30,

684.90
Nov. 20,

500.00 Sept. 25,

365.30 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

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per cent. ?

Dr.

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

Cr.

1856.

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18.15
48.26
91.20
30.00

90.10 12.50 20.00 25.00

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1856. March 1, To merchandise, $ 36.25

April 1, By cash, $ 48.25 April 7,

May 20, June 15,

June 17, July 21,

July 4, Aug. 1,

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

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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16 cash, • draft, 6 cash,

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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,

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 6mo., 846.00 | April 17,

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

100.00 July 30, 400.00 Aug. 15,

800.00 Sept. 12, m'dise on @mo., 560.00 Sept. 18, “ m’dise on 6mo., 630.00 Dec. 18, 600.00 Oct. 28, cash,

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.

66

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56 cash,

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

cente Ans. $ 430.04.

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