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6. If one note should be given for the following three, when should interest commence upon it?

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7. What is the mean time for the payment of the following bills of goods purchased by Calrow & Co. of Armstrong & Co.?

1856. June 1, a bill of $200 on 90 days.

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8. What is the equated time for paying the following?

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9. Find the equated time for the payment of the following notes held by Page & Son against Washington Manufacturing

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AVERAGE OF ACCOUNTS.

313. To AVERAGE AN ACCOUNT.

ILL. EX. I have in my ledger an account with F. E. Clarke, both the debt and credit sides of which consist of sundry items. The footing is as follows:

Dr. side $250, averaging due Feb. 9, 1863; the Cr. side $300, averaging due Apr. 4, 1863; at what time should I pay Clarke the balance?

Assuming, as in Art. 312, Jan. 31, 1863, as the time for settling this account, we compute interest on each item from this time till it is due. By settling Jan. 31, 1863,

I should lose 63 days' int. on

$300 $3.15

Clarke would lose 9 days' int. on $250 = $.375

The balance due Clarke is

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$50. $2.775 int., my net loss.

11 m. 3 d.

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If, by settling at the assumed date, my net loss of interest would be $2.775, I shall be entitled to keep the balance, $50, till it has gained $2.775, which, found by dividing it by the interest of $50 for 1 month, is 11 m. 3 d.; this added to Jan. 31, 1863, is Jan. 3, 1864, Ans.

If, however, the dates were transposed, making Clarke's $250 due to me Apr. 4, and my $300 due to Clarke Feb. 9, by settling at the assumed date Clarke would lose 63 days' interest on $250 $2.621,

I should lose 9 days' interest on

The balance due Clarke is

300= .45

$50. $2.17 int., C.'s net loss.

If, by settling at the assumed date, Clarke's net loss of interest is $2.17, he may justly require me to pay the balance, $50, at such time prior to Jan. 31, 1860, as will be required for $50 to gain $2.17 of interest, which is 8 m. 21 d.; this, reckoned back from Jan. 31, 1863, is May 10, 1862.

From the above example we deduce the following

RULE. To equate an account: Assume that all the items are to be paid on the last day of the month previous to the earliest day at which any item becomes due; find the interest on each item from the assumed date to the date at which it becomes due; find the difference between the interest on the Dr. and Cr. sides of the account; divide this difference by the interest on the balance of the account for 1 month; add the quotient to the assumed date when the larger side has the more interest, and subtract it from the assumed date when the larger side has the less interest.

314. Settlement can be effected earlier than the equated time, by deducting interest from the balance of the account for the time between the equated time and the desired time of settlement. It can be effected later by adding interest. The latter will be necessary when the equated time is already past. Or,

315. If it be desired to settle an account at a specified time, add interest to the items due before the specified time, and subtract interest from those due after the specified time; the difference between the total of the Dr. and Cr. items plus or minus their interest, will be the balance due.

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1. When can the balance of the following ledger account be paid without loss to either party?

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Balance of, $368 Bal. of int., $3.188

1% of $3681.84; 3.1881.84 1.73 = 1 m. 22 d.
Mar. 311 m. 22 d. Ans. May 22, 1863.

2. Add 3 months' credit to each item in the following, and

equate the .

DR.

1863.1

A. B. in with C. D.

1863.

Jan. 1 To Bal. Ledger B., $5000 Mar. 3 By Mdse.,
Mar.31" Real Estate,

May 30"

do. do.

66

50 00 May 27"

CR.

$50 00 50 00

55 00

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4. When is the balance of the following account due ?

DR.

DAY, WILCOX, & Co.

CR.

1864.

Aug. 15"

1864.

July 21 To Mdse., 90 da., $173 15 June 25 By Mdse.,

do. 60 da.,

13 68 June 30"

do.

30 da., $500 00 60 da., 5271

Aug. 31"
Oct. 17"

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317. To find the equitable time for the payment of the balance of a debt, when partial payments are made before the deb

is due: Make the whole debt the Dr. side of an account, and the partial payments the Cr. side.

5. A holds a note against B, dated Nov. 14, 1864, for $620, due 7 months hence, without interest. On this note B paid A $220 Jan. 14, 1865, and $100 Feb. 14, 1865; what is the equated time for paying the balance? Ans. Nov. 16, 1865. 6. T. Ropes owes R. Treat $250, due May 29. If he should pay $50 on the 29th of April previous, when should he pay the balance?

Ans. June 7.

7. A farmer purchased, on the 1st day of April, 1864, 3 acres of land at $183 per acre, agreeing to pay for it in 7 months; if he should pay $50.75 at the date of the purchase, $148.25 in 4 months, and $150 in 3 months, in what time should he pay the balance?

8. A owes B $2000 Oct. 5; if he should pay $1200 of it Sept. 8, at what time should the balance be paid?

9. J. Edwards owes J. Adams $1200 on a note dated Oct. 9, 1863, payable in 4 months without interest; if Edwards should pay Adams $250 on this note Jan. 16, 1864, and $400 Feb. 9, 1864, when should the balance of the note be paid?

10. Bought a lot of land for $800, for which I gave my note, dated May 7, 1864, payable in 6 months; June 28, I paid $158; Aug. 7, I paid $320.60, and Sept. 7, $179.40; when should the balance be paid?

11. Find the equated time for the settlement of the following

account:

ROBERTSON & REYNOLDS in % with JAMES LORING & Co.

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$562 17 July 18. By Cash,

$480 00

66 20.

Mdse. on 4 mo. 1524 82 66 27. Note on 90 d.

1218 65

Aug. 8. "
Sep. 30. "

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Nov. 25." Bill due,
Dec. 1." 66

66

Aug. 20." Real Estate,

286 58 Oct. 28. "Draft at 60d.†
424 60 Dec. 1. "Cash,

For Dictation Exercises, see Key.

210 00

600 00

783 25 Sep. 30. "Cash,

459 59

425 00

185 20

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