of 18 feet 6 inches in circumference, make, in running 150 miles.? Ans. 42810, and 5 yd. left. 29. How many times will a wheel, which is 9 feet 2 inches in circumference, turn round in going 65 miles? Ans. 37440. 30. If a man can travel 39 miles 20 rods a day, how long would it take him to walk round the globe, the distance being about 25000 miles? Ans. 640 days. 31. How many steps, of 30 inches each, must a person take in walking 21 miles? Ans. 44352. 32. How many suits of clothes, each containing 5 yards 1 quarter, can be cut out of 168 yards? Ans. 32. 33. How many coat patterns, each containing 2 yards 1 quarter 1 nail, can be cut out of 39 yards 1 quarter 1 nail? Ans. 17. 34. How many times can a vessel, holding 4 gallons 2 quarts, be filled out of a hogshead of wine? Ans. 14. 35. A man distributed £3 3 s. 9 d. among a company of boys, giving each 3 s. 9 d.; how many boys were there in company ? Ans. 17. N. B. The last four problems correspond to Note under Art. 22. SIMPLE INTEREST. ART. 89.) SIMPLE INTEREST is a sum allowed for the use of money, goods, or property. The sum, for which interest is allowed, is called the principal. The rate of allowance for 100 dollars, for 1 year, is called the rate per cent.-per cent meaning per 100. The amount is the principal and interest, added together.* *The rate of interest is, .in almost all countries, established by law; and asking, or taking more than such rates, is termed usury, and is subject to legal penalties. In New England and Ohio, the legal rate is 6 per cent., in New York 7; but in many countries of Europe, money can be obtained at 4 and 5 per cent. Every question of simple interest, is properly an example in proportion, or the Rule of Three. Three terms are given to find a fourth term. Thus: let it be required to find the interest of any sum, say $240, for 1 year, at 6 per cent. The term 6 per cent. means that 100 dollars yields 6 dollars in one year; and 240 dollars must yield in that proportion. Hence, as 100: 240 :: 6 to a fourth term, 6 14,40 This gives $14,40 for one year's interest; and if the interest were required for two or three, or more years, we should multiply this sum by 2, 3, or more, as the case may require; hence we have the following GENERAL RULE. Multiply the principal by the rate per cent., and that product by the time, (a year being the unit,) and divide by 100. Let the pupil remember that this is a general and universal rule, equally applicable to any per cent. or any required time, and all other rules must be reconcilable to it; and, in fact, all other rules are but modifications of this. (ART. 90.) When the interest is 6 per cent., we may multiply the principal by half the number of months, and divide by 100. Let us reconcile this rule with the former. What is the interest of $300 for 16 months, at 6 per cent.? As a year is the unit of time, we must divide the 16 by 12, to bring it into years and parts of a year; or the result must be the same, if we multiply by 16 and divide by 12 (Art. 24). Hence, by the General Rule, and under the form of Art. 24, we have 300=principal. 12 16=time. 100 Now cancel 6 in 12, and the quotient 2, into 16; it will That is, multiply the principal by half the number of months, and divide by 100. (ART. 91.) When the rate of interest is 4 per cent. multiply the principal by the number of months, and divide by 109. Let us investigate this rule. What is the interest of $720, for 2 years and 6 months, at 4 per cent.? Take the general rule: thus, When thus far canceled, the remaining part of the operation, put in words, is the rule above cited. In this way, we can show that 3 per cent. may require us to multiply by of the number of months, and divide by 100; 2 per cent. corresponds with of the number of months; and 1 per cent. with of the number of months, &c. (ART. 92.) When the per cent. is complex or mixed, as, 41, 53, 73, &c., it may be most convenient to first cast the interest at 1 per cent., by multiplying the principal by of the number of months, and dividing by 100; and afterwards, multiplying by the per cent., whatever it may be; or we may proceed by the general rule. The first will be most brief, if the months will divide by 12, or if we find any large common factors, between 100 and the months. N. B. When days are in question, they must be considered as parts of a month, 30 days to a month; therefore, 3 days is,1 of a month, 6 days,2, 9 days,3, &c.; or, in vulgar fractions, 1 day is '‰, 2 days 15, &c. EXAMPLES. 09 1. What is the interest of $75, for 1 year 6 months and 12 days, at 6 per cent. ? y. m. d. 1 6 12 18,4 months, half 9,2. By rule (Art. 90)— 100 | #$ 3 4)27,6 $6,90 Ans. 2. Find the interest of $467,17 for 3 years 5 months, at 7 per cent. This had better be done by the general rule. 3. Required the interest of $64,50 for 3 years 5 mon. and 10 days, at 7 per cent.? The days here make the operation more brief, if we take the canceling form, and cast the interest at 1 per cent. (Art. 92.) 4. What is the interest on $125, for 17 days, at 6 per cent.? First find the interest for 15 days, of one month, (Art. 90.) 4 | 12 5 days; 5 That is of a dollar, or ,31 cents is the interest for 15 of this in addition will give the interest for 17 Ans. 35 cents 4 mills. 5. What is the interest of $204, for 40 days, at 6 per cent.? days. 6. Find the interest on $420, for 2 years 1 month and 27 days, at 6 per cent. Time 25,9 months, 2 | 420 21 100 25,9 25,9 21 259 518 10)5439 $54,39 Ans. 7. What is the amount of $560, for 9 months and 20 days, at 6 per cent.? Ans. $587,066+ 8. What is the interest of $50,11, for 1 year and 21 days, at 6 per cent.? Ans. $3,18+. 9. What is the interest of $340,50, for 3 months, at 6 per cent.? Ans. $5,11. 10. What is the interest of $180, for 1 year 2 months and 6 days, at 6 per cent.? Ans. $12,78. 11. What is the interest of 25 dollars, for 3 years 6 months and 20 days, at 6 per cent.? Ans. $5,331. |