8. Purchased of a merchant, at different times, the follow

ing bill of goods:

Feb. 14, to the amount of $600 on 6 mo credit.

Required the equated time for the payment of the bill. Ans. Equated time, Oct. 15.

4. I sold goods to Mr. Bowman at different times and terms of credit, as follows:

July 16, 1862, a bill of $800 on 3 mo. credit.

If he gives me his note for the amount, when, in equity. should it begin to bear interest?

Ans. Feb. 23.

CASE III.

601. When a debt due at some future time has received partial payments, to find when the remainder should be paid.

1. A borrows $3000 to be paid in 8 mo.; 5 mo. before i was due he paid $800, and 2 mo. before it was due he paid $600; bow long after the expiration of the 8 mo. may the balance remain unpaid?

SOLUTION.-A credit on $800 for 5 mo. is equivalent to a credit on $1 for 4000 mo.; a credit on $600 for 2 mo. is equivalent to a credit on $1 for 1200 mo.; and adding, we have a credit on $1 for 5200 mo.; hence $1600, the sum which remains unpaid, . should have a credit of of 5200 mo., which is 3 mo. Hence

OPERATION.

800 x 54000 600 X 21200

1400

5200

5200

= 3mo.

1600

Rule.-Multiply each payment by the time it was paid be fore it was due, and divide the sum of the products by the sum remaining unpaid.

WRITTEN EXERCISES.

2. A borrowed $2400 to be paid in 6 mo.; 4 mo. before

being due he paid $600, and 3 mo. before due he paid $1200; at what time in equity should the remainder be paid? Ans. In 10 mo.

3. I lent Mr. C. $1600 for 9 mo., of which he paid in 5 mo., and of the remainder in 6 mo.; how long, in equity, may the remainder remain unpaid?

Ans. 11 mo. after due. 4. I borrowed of Mr. W. $400 for 3 mo., $600 for 5 mo., and $800 for 6 mo.; at the end of 4 mo. I paid him $1200; at what time in equity should the remainder be paid?

Ans. 7 mo. after borrowing.

5. A milliner bought of Smith & Co., a bill of $240 for 20 days, and $560 for 30 days; at the end of 16 days she paid $300, and at the end of 24 days she paid $350; when, in equity, should the balance be paid? Ans. 56 days.

AVERAGING ACCOUNTS.

602. Averaging an Account is the process of finding the mean or equitable time for the payment of the balance of the account.

1. In the following account, required the balance and the time when due :

Hence the balance is $350, and is due 23 da. after May 10, that is, on

June 2d.

SOLUTION. Select the date of the item first due as the focal date, and find the time the others are due after it; then multiplying each item by the corresponding time, and taking the sums of the products, we find that if paid on the 10th of May the Dr. items must suffer a discount of $1 for 49400 days, and the Cr. items must suffer a discount of $1 for 41500 days. Subtracting the two sums we find that the Dr. side must suffer a discount of $1 for 7900 days more than the Cr. side, hence $350, the Dalance of the items, must suffer a discount of of 7900 days, which is 22 days. Hence the balance is due 23 days after May 10th, or June 1st. Hence we have the following

Rule.-I. Find when each item is due, take the earlies date as the focal date, find the difference between the focal date and the remaining dates, and multiply each item by the corresponding difference.

II. Balance the columns of products and also the columns of items, and divide the former by the latter: the quotient added to the focal date will give the equated time.

III. If the two balances be on opposite sides of the account, the quotient obtained must be subtracted from the focal date.

NOTES.-1. Other dates than the earliest might be selected as the focal date. If we reckon from the last date we have the interest instead of the discount.

2. Instead of products we may obtain the interest at any per cent. on each item, and divide the balance of interest by the interest on the balance of the account for one day; the quotient will be the number of days to be added to or subtracted from the focal date.

WRITTEN EXERCISES.

2. What is the balance of the following account and when is it due? Ans. Balance, $450; due Jan. 23d.

3. What is the balance of the following account, and when is it due?

Ans. Balance, $205; due July 31st.

4. The following account was settled by Mr. Kready giv ing his note for the balance; required the face of the note and the time when interest commenced.

5. What is the balance of the following account, and if note is given, when does interest begin?

DR.

1872.

Ans. Balance $900; Int. from Dec. 18, 1871.

SMITH, IN ACC'T WITH BRAdford.

CR.

1872.

SETTLEMENT OF ACCOUNTS.

603. An Account Current is a written statement of the debit and credit items of business transactions between two parties.

604. The Adjustment of an account is the determining of the balance due at a specified date.

605. An account is Settled upon payment of the adjusted balance, or by carrying it to another account.

In finding the cash balance, interest should be allowed on each item for the time between the day it is due and the day of settlement.

Rule.-I. Find the interest on each item from the time it becomes due to the date of settlement.

II. Add the interest to the item if due before the date of settlement, and subtract it when the item is due after the date of settlement. The difference of the sums of the results on both sides of the account will be the cash balance.

NOTES.-1. An account may be adjusted by averaging it and finding the amount of the balance from the time it becomes due till the time of settlement.

2. In averaging an account, we find at what date the balance is due; in ad Justing an account, we find what balance is due at a specified date.

WRITTEN EXERCISES.

1. Required the cash balance of the following account, July 16, 1875, interest at 6 per cent. Ans. $200.60.

2. Required the cash balance of the following account,

606. An Account Sales is a written statement, rendered by an agent or consignee to the consignor, of the sales of goods consigned, the charges, and the net proceeds.

607. Guaranty is a charge made for securing the owner against the risk of non-payment, when goods are sold on credit.

Expenses incurred in receiving the goods and all charges paid in cash are considered due the consignee when paid, but commission and after charges are due at the average maturity of the sales.

An account-sales is averaged to find when the net proceeds become due, in order that the consignor may draw a bill of exchange to fall due at the equated time. Except that the date of maturity of the commission and guaranty must be found by first averaging the sales, the account is averaged like an account current, the charges being the debits and the sales the credits.

1. Account sales of 400 barrels of pork received from Gibbs and Waterman of Chicago to be sold on their % and