238
ARITHMETIC.
Common (Fay.
92-41035)2508 - 928,06(27" 149866072106138486104607575091116100794678505539570
Contracted.
92-4103,5)2508-928,06(27'1493660721138494608912806
(49.) Role I. To reduce a Vulgar Fraction to an EquivalentDecimal.
Divide the numerator by the denominator, as in division of de-cimals, and the quotient will be the decimal required.
Examples.
3 12 3
— = -375 — = • 16 — = -044776
8 75 67
Examples.
Reduce L. 3 :
12: 6Id. to the denomination of pounds.4 I 3
12
20
6-75
12-5625
3-628125 Ans.Reduce 6 yds. 3{. to yards.
8 5'
4 3-6256.90625
Interest.
(52.) Interest is the premium allowed for the loan of money.
The sum lent is called the principal. The sum of the principaland interest is called the amount.
Intere st isallowed at so much per cent, per annum, or the interestof L. 100 for a year, is called the rate of interest.
Interest is of two sorts, simple and compound.
Simple Interest.
(53.)Simple Interest is that which is allowed for the principallent only.
Rule 1. To find the interest for a year, multiply the principalby the rate, and divide the product by 100.
2. To find the interest for several years, multiply the interest ofone year by the number of them.
3. To find the interest for any parts of a year, as ,J, 3, &c. takethe same proportional parts of one year’s interest.
4. For any number of days, multiply the interest of a year bythem, and divide by 365.
Example.
(50.) Rule II. To reduce a Decimal of a Superior Denominationto its Value in the Inferior Ones.
Multiply the given decimal by such a number as will reduce itto the next inferior name, and point off in the product as manyplaces of the decimals as are in the given number; then reducethese in the same manner to the next name ; and thus continuethe reduction to the lowest name required, or till the decimalspointed off be all cyphers ; then the numbers on the left of thepoints will express the value of the decimal.
Example.
What is the value of -775 of U.
•77520 -
What is the interest of L. 225. 10s. for 6J years, at 4( per cent,per annum ?
225-5 principal4-5 rate
100)1014-75
10 1475 interest for a year6
60-8850 interest for 6 years2-536875 interest for year
63-421875
or 1 .63 : 8 : i>id. the interest required.
sh. 15-50012
d. 6 000
(51.) Rule III. To reduce Integers or Decimals to EquivalentDecimals of Superior Denominations.
Case I. If a simple number or decimal be proposed, re-duce it to the name required, by dividing as in reduction ofntegers.
Example.
Reduce 9d. to the decimal of a pound.
12 ) 9.00
20).7500.0375
Case 2. A compound number may be reduced to a superiorname, by reducing each of its parts, and taking the sum of thedecimals; the best way to do which is this: write the givennumbers under each other, proceeding orderly from the least tothe greatest name, for dividends; draw a perpendicular line onthe left of these, and on the left of it write opposite to each divi-dend such a number, for a divisor, as will reduce it to the nextsuperior name ; then begin with the upper division, and affix thequotient of each to the next dividend, as a decimal part of it, be-fore it be divided, and the last sum will be the answer.
The above rules for simple interest serve also to calculate Com-mission, Brokage, Insurance , the Stocks, or any thing else ratedat so much per cent.
(54.) Compound interest is that which is allowed, not only forthe sum lent, but also tor its interest; as it becomes due at the endof each stated time of payment.
Rule. Find the amount of the given principal for the time ofthe first payment, by simple interest ; then consider this amount asthe principal for the second payment, whose amount calculate inthe same manner ; and so on through all the payments, still ac-counting the last amount as the principal of the next payment.
Example.
What will L. 50 amount to in 3 years, at L. 5 per cent, per an-num compound interest ?
To 50 principal
add 2-5 interest for 1 year
52-5 principal for second payment2-625 interest
55-125 principal for 3d payment2-75625 interest
or L. 57 : 17? 7$ H° Unt ret » uirctL