RULES AND TABLES.

PART II.

PERCENTAGE.

CASE I.

MULTIPLY the given number, or base, by the rate expressed decimally; the product will be the percentage.

CASE II.

Divide the percentage by the base, extending the division to hundredths.

CASE III.

Divide the percentage by the rate expressed as a decimal.

INTEREST.

CASE I.

Multiply the principal by the rate per cent. expressed decimally, and the product will be the interest for one year. If the time is in years and months, multiply this product by the time expressed in years and the fraction of a year. If the time is in years, months, and days, take of the year's interest, and multiply it by the time expressed in months and the fraction of a month.

NOTE.-Unless otherwise specified in the examples, 6% is to be taken as the rate, 30 days as a month, and 12 months as a year.

BUSINESS METHOD.

Multiply the principal by the number denoting the time in days, and divide the product by 6, pointing off three figures in the quotient when the principal is in dollars only, and five figures when there are cents in the principal.

NOTE.-For any other rate than 6%, multiply the interest at 6% by the given rate, and divide by 6.

CASE II.

Divide the given interest by the interest of one dollar for the given time and rate; or, divide the given amount by the amount of one dollar for the given time and rate.

CASE III.

Divide the given interest by the interest of the given principal for the given time at one per cent.

CASE IV.

Divide the given interest by the interest of the given principal at the given rate for one year.

COMPOUND INTEREST.

Find the amount of the given principal for the first period for which it is to be compounded, proceed with this amount as a new principal for the second period, and so on; the difference between the last amount and the given principal will be the compound interest.

FIND the interest on the given principal from the date of the note to the date of the first payment, and if this payment equals or exceeds the interest, subtract it from the amount then due, and proceed in like manner with the remainder as a new principal.

If any payment is less than the interest due, find the in

terest on the last principal to the date of the next payment, and so continue until the sum of the payments equals or exceeds the interest due; then subtract the sum of the payments from the amount due, and proceed as before.

(MERCANTILE RULE.)

Find the amount of the note or debt from the time it begins to draw interest, to the time of settlement; also the amount of each payment, from its date to the time of settlement.

Add the amounts of the payments together, and subtract their sum from the amount of the note or debt.

PRESENT WORTH AND DISCOUNT.

Divide the debt by the amount of one dollar for the given time and rate; the quotient will be the present worth.

Subtract the present worth from the debt, and the remainder will be the discount.

BANKING.

CASE I.

Find the interest on the face of the note for three days more than the time specified, and the result will be the bank discount.

Subtract the discount from the face of the note or sum discounted, and the remainder will be the proceeds.

NOTE. In discounting notes the banks of Pennsylvania, Delaware, Maryland, Missouri, and Washington City charge interest for the day on which the notes are discounted and the day on which they mature. For example, a note drawn October 3, 1876, for 3 months, and discounted November 3, 1876, matures January 6, 1877, and the term of discount is from November 3 to January 6, both inclusive, or 65 days.

CASE 11.

Divide the given proceeds by the proceeds of one dollar for the given time and rate; the quotient will be the face of the

note.

PROPORTION.

SIMPLE.

EXPRESS the ratio of the terms which are of the same kind, as a proper fraction when the answer requires to be less than the remaining term, and as an improper fraction when the answer requires to be greater; multiply by the term which is of the same kind as the required answer, and the product will be the fourth term or answer.

COMPOUND.

Express the ratio of each pair of terms that are of the same kind, as a proper fraction when the answer, considered with reference to that pair, requires to be less than the term which is of the same kind as the answer, and as an improper fraction when the answer requires to be greater; and multiply the product of these fractions by the term which is of the same kind as the answer.

PARTNERSHIP.

SIMPLE.

MAKE the whole gain or loss the numerator, and the whole capital the denominator of a fraction; multiply this fraction by each partner's capital, for his share of the gain or loss.

COMPOUND.

Multiply each partner's capital by the time it is employed. Make the sum of all these products the denominator of a fraction, and the total gain or loss the numerator. Multiply this fraction by the product of each partner's capital by the time it is employed, and the result will be each partner's share of the gain or loss.

EQUATION OF PAYMENTS.

CASE I.

MULTIPLY each debt by the number denoting its term of credit, and divide the sum of the products by the number denoting the sum of the debts; the quotient will be the average term of credit. The average term of credit, added to the date of the debts, will give the equated time.

CASE II.

Multiply each payment by the number denoting the time it was paid before becoming due, and divide the sum of the products by the number denoting the balance unpaid; the quotient will be the time the balance should be kept after maturity.

CASE III.

Multiply each sum by the number denoting the difference in days between the date on which it becomes due, and the latest date on which any sum named in the account becomes due; divide the sum of the products by the sum of the debts, and the quotient will be the number of days to be counted backward from the latest date.

AVERAGING OF ACCOUNTS.

To find the equated time, multiply each item of debit or credit by the number which denotes the difference in days between the date on which it becomes due, and the latest date on which any item in the account becomes due.

Divide the difference between the sum of the debit and the sum of the credit products by the difference between the sum of the debits and the sum of the credits, and the quotient will be the number of days to be counted forward from the latest date when the larger sum of products is on the smaller side of the account, or backward when the larger sum of products is on the larger side of the account.