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3. Equation of Payments.

A problem of great frequency and importance in business is to find the equated time or date when the sum of several debts due at different times may be paid.

The term of credit is the time to elapse before a debt is due.

The equated term of credit is the time to elapse before the sum of several debts due at different times is due-reckoned from some arbitrary zero date.

The equated time is found by adding the equated term to this convenient arbitrary zero date.

The zero date is generally either the first date of any bills due or the first day of the month in which the account begins.

The latter date is in general the more convenient.

The cases are three in number:

"To find the equated time of bills bought (1) for unequal times at different dates, (2) for equal times at different dates, (3) for unequal times at the same date."

(1)For bills at different dates for unequal times,"
Convert times into days, using convenient zero date.
Multiply each item by its term of credit in days.
Add the items and these products.

Divide the sum of the products by the sum of the items.

The answer will be the equated term in days.

Add this to the zero date to obtain the equated time.

(2) "For bills at different dates for equal times,' we may proceed as in the above rule or find the equated time for the dates alone, adding on the term of credit afterwards.

EQUATED PAYMENTS.

201

(3)

"For bills at the same date for unequal times," the given date should be taken as the zero date.

Note. Use the Table of Days throughout.

If months and fractions of a month (30 days to the month) are employed the work is less, but the results are not so accurate always.

Example. The equated time of the following bills.

1890

1920

Ap. 4. To merchandise 6 mos. credit £320 × 186 2560

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4. The Averaging and Balancing of Accounts.

An Account is the statement of business transactions between debtor and creditor.

Averaging Accounts is the process of finding the date on which the balance is due (i.e. the equated term of the balance from some zero date).

A Balance is the difference of the two sides of an account.

A Cash Balance differs from the balance by the interest due or the discount claimable.

The creditor receives interest on the balance from the date on which it is due to the date of settlement.

The debtor is entitled to discount off the balance for the time he pays it before the date on which it is due.

1°. Rule for Averaging Accounts.

Multiply each sum on both sides by its term of credit in days-reckoned from a convenient zero date. Add the amounts and the amounts multiplied by the days on each side-all four separately.

Find balance of the account and also the difference of the amounts × the days on the two sides.

Divide this difference by the balance.

The answer will be the equated time in days from the zero date.

If the balance of the products is in favour of the debtor side-the equated term must be added to the zero date to get the date on which the balance is due, and if it is paid before this date discount is allowed.

If the balance of the products is in favour of the creditor side-the equated term must be subtracted from the zero date to get the date on which the balance was due, and interest is charged from this date to the date of payment.

2°. Rule for finding the Cash Balance at any date.

Multiply each sum on both sides by the difference in days between its date and the date of striking the cash balance.

Add the amounts and these products on both sides -all four separately.

Find balance and difference of products.

The difference of products ×

rate of interest

gives

interest due or discount claimable. from balance-for the cash balance.

36500 Add to or subtract

If the balance of products is in favour of the debtor side-interest must be added.

If the balance of products is in favour of the creditor side-discount may be subtracted.

CASH BALANCES.

203

3°. Rule for monthly statements (cash balances at the end of the month).

Multiply each item by the difference in days between the date and the end of the month.

Add the amounts and the products.

The products ×

rate of interest

36500

gives interest due.

Add to balance this interest for the cash balance.

Note. For all these operations use the Table of Days.

Less work is involved in working with months and decimals of a month (30 days), but the results are not so accurate.

Example 1. Averaging accounts.

To find the equated time of paying the balance of this account :

:

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The products are in favour of the debtor side.

.. the equated term must be added to the zero date.

Thus the equated time is Nov. 10, 1890.

The work may be shortened by calling £641. 12s. 74d. £642, and £650. 9s. 6d. £650, and £372. 88. 9d. £372-the same result is obtained as to time here, but this is not always the case.

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The products are in favour of the credit side.

.. the equated term must be subtracted from the zero date. Thus the balance was due on Sept. 15, 1888.

Note. This may seem peculiar, but the debtor had 76192 days from June 1, 1889 to pay £1 by the terms of the transaction, whereas he actually took 181346 days to pay it (105154 days too much). Hence as compensation he should have paid the balance (£406) 259 days before June 1, 1889, since 406 × 259 = 105154.

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