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210. The Focal Date is the date from which we begin to reckon in averaging an account.

WRITTEN EXERCISES.

1. A owes B $70 due in 4 months, and $80 due in 6 months; what is the average term of credit?

ILLUSTRATION.

4 mo.

$70

$80

6 mo.

$600,

66

ILLUSTRATION.

June 10th-4 mo.

Aug. 5th.

150

70 × 4
80 × 6

5 mo. 2 da.

$150

5 mo. 2 da., Ans.

A credit on $70 for 4 mo. is equivalent to a credit on $1 for 280 mo. A credit on $80 for 6 mo. is equivalent to a credit on $1 for 480 mo. Adding, A is entitled to a credit on $1 for 760 mo.; hence he is entitled to a credit on $150 for as many months as 150 is contained times in 760, which is 5 months, or 5 mo. 2 da.

$700, Aug. 1st-3 mo.

Total, $1800-56 da.

2. I purchased the following bill of goods:

66

May 5, a bill of $500 on 3 mo. credit,
June 10,
Aug. 1,
When can I settle these bills in one payment without loss to
either party?

$600 on 4
$700 on 3

$500, May 5th-3 mo.

PROCESS.

280

480

66

=

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=

)760(5 mo. 750

10 =

2 da.

Oct. 10th.

Nov. 1st.

...... Sept. 30th, Ans.

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$300 140

$160

00000
39600

61600
)101200(56+

90

112

108

=

56 da. after Aug. 5, which is Sept. 30, Ans.

$300-8 mo.

of 56 days after Aug. 5, which is Sept. 30.

3. A owes $300 due in 8 months; if he pays $80 in 3 months and $60 in 6 months, when should he pay the balance?

$140

PROCESS.
80 x 5400

60 × 2 = 120

These bills begin at different dates and are due at different dates; hence, to average them, we select the earliest date at which any of the bills become due (Aug. 5) from which to reckon times.

The second falls due Oct. 10, and the third Nov. 1.

$80-5 mo.

From Aug. 5 to Oct. 10 is 66 da.
From Aug. 5 to Nov. 1 is 88 da.
Proceeding as in Ex. 1, we have a credit

ILLUSTRATION.

40 160

160)520(3 mo.
480

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$60-2 mo.

Hence he is entitled to the use of the balance, $160, long enough after it becomes due to equal $1 for 520 mo., which is T of 520 mo., or 3 mo.

Balance $160 Due in 3 mo., Ans.

By paying $80 5 mo. before it is due and $60 2 mo. before it is due, A loses an equivalent of $1 for 520

mo.

4. M owes $400 due in 5 mo., $500 due in 6 mo., and $600 due in 7 mo.; what is the average term of credit?

5. Mr. Bowman bought goods as follows: Mar. 15, $300 on 2 mo. credit; Apr. 10, $400 on 3 mo. credit; May 5, $500 on 4 mo. credit; what is the equated date of payment?

6. B sells goods to C on credit of 60 days as follows: Jan. 14, 1894, a bill of $2000; Feb. 10, 1894, a bill of $1500; Mar. 25, 1894, a bill of $3000; find the equated time and date of payment.

7. B borrowed $1200 for 6 mo.: at the end of 2 mo. he paid $400, and at the end of 4 mo. he paid $600; when should the balance be paid?

8. What is the average time of paying $120 due in 5 mo, $150 due in 6 mo., and $160 due in 4 mo.?

9. What is the date of paying $60 due May 18, $130 due June 24, and $180 due Aug. 1?

10. I gave B $12000 for 10 mo., mo., and of the remainder in 6 mo.; ance remain unpaid?

11. A merchant owes $2200 due in 9 mo.; if he pays $800 in 3 mo., $600 in 5 mo., and $400 in 7 mo., how long in justice may the balance remain unpaid?

of which he paid in 4 how long may the bal

12. I sold goods to Mr. Martin as follows:

Oct. 14, 1893, a bill of $600 on 3 mo. credit;

66

Nov. 20, 1893,
Dec. 16, 1893,
Jan. 24, 1894,

$500 on 4
$400 on 3
$350 on 6

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66

66

66

Find the date of payment.

13. A owes $800 due in 5 mo., $1200 due in 7 mo. ; if at the end of 5 mo. he pays $1400, when should the balance be paid?

14. Three 90-day notes bear date as follows: Apr. 10, 1894, $480; May 12, 1894, $520; June 14, 1894, $640. What is the average date of payment, counting three days of grace?

15. A sells B goods as follows: $200 in 90 days, $300 in 60 days, $400 in 30 days, $500 in 10 days, and $600 cash; what is the average term of credit?

16. A merchant owes $3300 due in 8 months; if he pays $1200 in 3 mo., $1000 in 4 mo., and $500 in 6 mo., when should he pay the balance?

AVERAGING OF ACCOUNTS.

211. Averaging of Accounts is the process of finding the time when the balance of an account may be paid with justice to both debtor and creditor.

WRITTEN EXERCISES.

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

Dr.

John H. Landis.

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Cr.

=

4100 15840

=

- 22320

42260 8640100863. In practice 86 da. Mar. 15+ 86 da. = June 9th, Ans.

The payment for the flour sold Apr. 20th on 2 mo. credit is due June 20th, and that sold May 28th on 1 mo. credit is due June 28th. The 15-day draft of May 24th is due 18 days after May 24th, or June 11th.

It will be seen that Mar. 15th is the earliest date at which any one of the items is due. Using this as the focal date, we find the sum of the products on the debit side to be equivalent to $1 for 50900 days, and the sum of the products on the credit side to be equivalent to $1 for 42260 days. Subtracting 42260 from 50900, there is a balance on the debit side equivalent to the use of $1 for 8640 days.

In order to make the products on the debit side equal to the products on the credit side, it is evident that the balance of $100 must be paid after the focal date, Mar. 15th. Now, for the credit of $100 to be equiv alent to $1 for 8640 days, it must have a credit of 86 days.

Hence the account can be settled by paying $100 86 days after Mar. 15th, or on June 9th.

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

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Dr.

6250

2400

8650

1890.

Aug. 18 To Mdse.,
Sept. 24

66

66

PROCESS.

Sept. 20, 100 × 00
Oct. 25, 300 × 35
$400

$100 00 "Draft, 30 da. 300 00

$450

400

$50

1850 ÷ 50

37 da. 37 da. back from Sept. 20th is Aug. 14th, Ans.

Solving this problem as Ex. 1, we find that the balances are on opposite sides of the account.

Cr.

Now, in order to make the products of both sides equal the credit of the balance, $50, for 37 days must be subtracted from the sum of the products on the credit side. This indicates that it should have been paid 37 days before the focal date, Sept. 20th, or on Aug. 14th.

It is evident from these examples that if the two balances are on the same side of the account, the equated time is after the focal date; if they are on opposite sides of the account, the equated time is before the focal date.

Samuel P. Hambleton.

0000 10500

3. Find the equated time for paying the balance of the following account:

1890.

$400 Sept.
800 Oct.

10500

8650

1850

1 By Cash,

66 12

66

Cr.

$350 650

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