PREDICTIONS.

ax b

7. Form

cx d'

145

Decide by inspection the number of integers or ciphers in the dividend and divisor and hence also the number in the quotient.

The number of places to which the dividend may have to be correct number of places required correct number of quotient integers or ciphers number of dividend integers or ciphers + 1.

The number of places to which the divisor must be correct = number of places required correct + number of quotient integers or ciphers number of divisor integers or ciphers + 1.

Example. 27-3125 × ·6134583÷17·321 ÷ 5·785 to 3 places.

These methods should be employed in all questions which involve one or more of the forms given. In every part of this book their use will greatly abridge the labour of calculation.

Examples will be found in the Metric Section and also under Proportional Parts, Partnership, and Interest.

The rules will be found to be specially valuable in Indirect Exchanges and Arbitrations.

The principles underlying the rules involving division are (1) that the number of figures correct in the dividend must be one more than or the same as the number of figures in the quotient, (2) that the number of figures correct in the divisor must be one more than or the same as the number of figures in the dividend.

The reason of the rule for a continued product will be obvious on reflection.

SECTION VII.

INTEREST, ANNUITIES, AND STOCKS.

1.

Interest.

Interest is money paid for the use of money lent for a certain time at a fixed rate.

The money lent is called the Principal.

The interest on £100 for a year is called the Rate per cent.

The sum of the interest and principal is called the Amount.

Simple Interest is interest reckoned on the principal alone.

Compound Interest is the interest accumulated from year to year by the addition of the yearly interest to the principal-the interest when added also bearing interest.

Any term may take the place of a year, e.g. a quarter or half-year.

In ordinary business simple interest is the only kind largely used-first, because the time of bills is usually less than a year but also because accounts are made up every half-year and any interest accruing is either paid or added to the balance; thus though this involves in reality the principle of compound interest yet the operation is rarely performed.

It cannot however be too clearly understood that money is always bearing interest when in use (i.e. lent or invested or put into business) or would bear interest if there was any profit.

CURRENT ACCOUNT.

Interest in Banks.

147

2. The Calculation of Interest is an important part of Banking business. The customs adopted vary somewhat but the leading principles are always the

same.

(1) Interest Tables are used to avoid labour and save time, and of these there are various forms.

Lawrie's tables are calculated at 2, 3, 3, 4, 41, 5 p.c. on every £1 up to £100, then every £10 up to £1000, every £100 up to £10000, every £1000 up to £100000 for 1 to 365 days.

For any intermediate rates devices are used to get them from the given rates.

31/2+3 18= 4

Ex. 1ğ

King's tables are for very large amounts for 1 day. There are other convenient tables, notably Rourke Jones', giving interest at rates proceeding by eighths.

In customers' accounts banks disregard or allow for the s.d.f. according as the s.d.f. are above or below 10s. in reckoning interest.

Banks never enter farthings as interest.

(2) For Current Accounts interest is calculated by "extending the Decimal" or "on the minimum monthly balances."

London banks give no interest on current accounts but do not charge for cashing cheques as a compensation.

Provincial banks give interest and charge for cheques.

The term "extending the decimal" is utterly misleading there is no decimal-the operation is simply that of multiplying pounds by days.

By this means the interest is reduced to that of a sum of money for 1 day.

An example will make it clear.

MONTHLY BALANCES.

149

When the books are balanced the decimals (socalled) are added up and interest on amount for 1 day at current-deposit rate is found and added to balance of the customer.

Similarly the decimal is extended in the case of overdrafts but the rate is much higher.

If there is a change in the rate two methods may be adopted.

(a) Add up decimal to date when rate changesfind interest and extend it in a further column-then begin again with your decimal for the new rate.

(b) Add up decimal to date and equalise it to new rate-then proceed with decimal as usual.

To equalise to new rate, add or subtract proportionally, e.g. 6 p.c. from 5 p.c. subtract of decimal."

Minimum Monthly Balances are the lowest amounts remaining to the credit of any customers during the month-on these interest is allowed by those banks which adopt the system. It finds favour with Scotch banks and some English banks.

(3) For deposit accounts interest is best calculated by forming a table of days from a certain date for the rate of interest transformed to 5

p.c.

Ex. 2 p.c. for 93 days = 5 p.c. for 33-2 days.

Shaw's Scotch tables are an instance.

The rate for deposits varies during the year to some extent as it depends upon the bank rate of discount.

(4) To average the income tax when rate has changed on Ap. 5.

Rule. Multiply days to Ap. 5 by old rate and days from Ap. 5 by new rate and divide by the total period of days of the interest wanted.