167. PER CENT: 59 QUESTIONS FOR PRACTICE. per cent. ? 2. What is the amount of 10. What is the interest of $175.62 for one year and six | £86 10s. 4d. for 1 year and 6 months, at 6 per cent. ? months, at 6 per cent. ? 175.62 prin. 86.5166 If the principal .06 rate. .06 be English money, the shillings, pence, €5.190996 &c. must be reduce 10.5372 one yr. int. 1.5 ed to the decimal 1.5 time. of a pound, (143), The decimals 2595-1980 then proceed as in 526860 below mills are 5190996 Federal money. The interest will be 105372 omitted in the Ans. £7.7864940 in pounds and answer to this decimal parts, which must be reInt. 15.80580 and the follow- duced to shillings, &c. (144). Pri. 175.62 ing questions. 11. What is the interest of £1 13s. 4d. for 1 year, at 9 Ans.191.425 amount. Ans. 3$ 3. What is the amount of 12. What is the interest of $10.15, on interest 12 years at £25 for 6 months, at 4 per 6 per cent. ? Ans. $17.458. cent. ? Ans. 10s. 4. What is the interest of 13. What is the amount of $48.643 for 2 years at 6 per $18.24 for 2yr. and 9mo. at 6 cent. ? Ans. $5.837. per cent. ? Ans. $21.249. 5. What is the interest of 14. What is the interest of $225.755 for 3 years, 8 months | $240.16 for 3yr. 5mo. 1d.? and 10 days, at 6 per cent. ? Ans. $49.272. Ans. $50.041. 15. What is the interest of What is the inter of $958.54 for 5 days, at 7 per $213.23 for 3 years and 12 cent. ? Ans. $0.925. days, at 10 per cent. ? Ans. $64.679. 16. What is the interest of $23.23 for 3 years, at 55 per 7. What is the interest of cent. ? $1600 for 1 year and 3 months, 54 per cent=.055. Ans. $120. Ans. $3.832.. 8. What is the interest of 17. What is the interest of $121.11, for 2 years and 7 £329 17s. 6d. 2qr. for 3 years, months, at 5 per cent. ? 7 months, and 12 days, at: 5 Ans. $15.643. £59 13s. O d. 9. What is the interest of 18. What is the interest of $174.18 for 2vr. 8mo. ? $537.246 for 1 year, at 6 per Ans. $19.868. cent. ? Ans. $32.234. at 6 per cent. ? per cent. ? SECOND METHOD. ANALYSIS. 168. 1. What is the interest of $60, for 5 months and 21 days, al 13 per cent. per annum ? If the interest of $1 be 12 cents for 12 months, the interest of $1 for 1 month will be 1 cent, for 2 months 2 cents, for 3 înonths 3 cents and generally the number of months written as só many cents, or hundredths of a dollar, will be the interest for that time. And as the interest of $1 for Ino. 330 days) is 1 cent, the interest for any number of days is so many 30ths of a cent, or 3ds of .057 rate. a mill. In the present example we write the 5 months as so many cents, or hundredths of a dollar, and dis 420 viding the days by 3, find of them to be 7, which 300 we write in the place of mills in the multiplier; and $60 multiplied by $0.057, (the interest of $? for the $3.420 Ans. given time,) the product, $3.42, is evidently the inter est of $60 for that time. 60 prin. 169. 2. What is the interest of $60 for 5 months and 21 days, al 6 per cent. per annum ? Since interest at 12 per cent. (168) is found by multiplying by the whole number of months and of the days, interest at 6 per cent. being of 12, may evidently be found by multiplying by half the former multiplier, that is, by half the months written as cents, and one sixth of the days written at the right hand. In the present example, half the 2) 60 months is 23, and if there were no odd days, we .028] should write down 2 cents, 5 mills, or 0.025 for the multiplier ; but when there is an odd month and days, 480) as in the present case, it is as well to call the odd 120 month 30 days, and adding thereto the odd days. 30 divide the whole by 6, the quotient (30+21:6=84) will be mills. $0.028; then is the interest of $1 for $1.710 Ans. 5 months 21 days, and 60 times $0.028., or $0.028.1 times 60, (86)=$1.71, is the interest of $60" for the same time. To multiply 60 by ), we take 1 of 60, or divide 68 by 2, and in general for the odd days, less than G, we take such part of the multipliand as the odd days are part of 6. Hence, 170. To compute the interest at 6 per cent. per annum upon any sum for any time. RULE Under the principal write half the even number of months, for a multiplier, (pointing them as so many cents, or hundredths of a dollar.) If there be an odd month, call it 30 days, to which add the odd days, if any, and, dividing them by 6, write the quotient in the place of mills in the multiplier. Multiply the principal by this multiplier, and the product, pra perly pointed, (122) will be the interest for the given time. NOTI.-Odd days less than 6 are so many 6ths of a mill, and to put ply by these, proceed as follows: 170. PER CENT. 61 For 1 day=1, divide the multiplicand by 6 3 2 “ twice by 3 “ by 2 and 3 and add the quotient, or quotients, to the product of the principal by half the months. yr. mo. d. 2) 215; QUESTIONS FOR PRACTICE. 3. What is the interest of 9. What is the interest of $75, for 4 months and 2 days, $49.25 for 3 years, 3 months, at 6 per cent. ? and 3 days? Ans. 9.628. 3)75 Here the months is .020.02, and as 6 is not con 10. A note for $500 on intained in the days, we terest, was dated Sept. 22, 1500 write a cipher in the 1820 : what was due, principal 25 place of mills, that the quotient, in dividing by and interest, July 29, 1823? Ans. $1.52513, may fall in its proper Ans. $585.583. place. There being 3 1823 6 29 decimal places in the factors, there 1820 8 22 must be 3 pointed off in the product. 4. What is the interest of 2 10 7 Timè. $215 for 1 month and 15 days? 11. What is the amount of Imo. 15d.=45d.; 6 in 45, 7 times $212 on interest for 14 months ? and 3 over. Ans. $226.84. 12. A note for $27.55 on two first decimal places 1505 107 must be supplied with interest, was dated Feb. 14, ciphers, and 7 must take 1823: what was there due, Ans. $1.612 the place of mills. The principal and interest, Jan. 20, use of the ciphers is to 1824? Ans. $29.092. guide us in pointing the product. 5. What is the interest of 13. What is the amount of $275.756, for 1 year, 9 months $87.91 on interest 3 and years and 15 days? Ans. $29.643. 27 days? Ans. $104.129. 6. What is the interest of 14. What is the interest of $137.84 for 2 years and 6 $607.50 for 5 years? months ? Ans. $20.676. Ans. $182.25. 7. What is the interest of 15. What is the interest of $575 for 8 months ? $655 for 7 days ? Ans. $23. Ans. $0.70%. 8. What is the interest of 16. What is the interest of $13.41 for 3 months and 16 $76.256 for 1 year, 3 months; days ? Ans: $0.236. and 5 days? Ans. $5.782. 171. When the interest is any other than 6 per cent.; first find the interest at 6 per cent., of w?:ich take such part as the interest required exceeds, or falls short, of 6 per cent, and this add. ed to, or subtracted from, tie interest at 6 per cent., as the case requires, will give the interest required. QUESTIONS FOR PRACTICE, 17. What is the interest of 18. What is the interest of $165.45, for 1 year and 6 mos. $5.98 for 2 years and 8 months, at 5 per cent. ? at 3 per cent. ? Ans. $0.478. 165.45 principal. .09 19. What is the interest of $45 for 6. months, at 8 per 6)14.8905 int. at 6 per cent. cent. ? Ans. $1 80. --2.4817 subtracted. 20. What is the interest of $10.15 for 12 years, at 3 per Ans. $124088 int. at 5 per cent. cent.? Ans. $3.654. VARIETIES IN SIMPLE INTEREST. per cent. ? 172. 1. What sum of money will amount to $31.35 in 9 months, on interest at 6 per cent. ? As the amount of $1 for 9 months at 6 per cent. is $1.045, the principal, which will produce any other amount at the same rate in the same time is evidently as many dollars as the number of times $1.045 is contained in that amount, and $31.35; $1.045=$30. Ans. Hence, I. The time, rate and amount being given, to find the principal. Rule.- Divide the given amount hy the amount of $1 for the given time and rate, and the quotient will be the principal required. 2. The amount for 8 months at 6 3. What principal will amount to per cent. was $598; what was the $1700 in 1 year and 3 months, at 3 principal ? Ans. $575. Ans. $1600. 173. 1. What principal will gain $1.35 in 9 months at 6 per cent. !, As $1 in 9 months will gain 80.045, as many dollars will be required to gain $1.36 in 9 months, as the number of times 1.35 contains 0.045 and $1,35; $0.015=$30. Ans. Hence, II. The time, rate and interest being given, to find the principal. RULE.-Divide the interest, or gain, by the interest of 1 dollar for the given time and rale, and the quotient will be the principal. 3. Whal principal will gain $100 in 8 months ? Ans. $575. in 1 year and 3 months, at 5 per cl. ? Ans. $1600. 174, 1. If 30 dollars gain 1 dollar 35 ccuts in 9 months, what is the rate per cent. ? 175, 176. At I per cent sur le preg me I czas w * rate, therefore, is so mu dres - Bez, a in the whole gen. 3 = . EL Ans. Hence III. The principes iztos eni same in a famo Rule.-D.side te gren arazs. in se wts vs Du at one per ceni. bu se sva ime, aut ise seduta i za ceut. 2. If the interest on 55 dulars for 8 months be B douz, e the rate per cent. ?. Ans. 6 per cent 175. 1. If the interest os 3 culla abre en gee awnin. so i dollar and 35 cents, what is the tisse! The interest on 30 dualars for 1 year a 5 oni I join at cems. Now, if the giren issetest be 21:31 to increase the 22 principal for one year, the quits our te se uue that principal was on interest-315-5163 sms stá the answer. Therefore, IV. The principal, rate and interut kosz zor, u sia fine RULE.—Divide the given interest by the interest of the grea princi for 1 year at the given rate, and the quotient will be the time is as and decimal parts. 2. If the interest on 575 dollars! 3. If the interest o 1510 din at 6 per cent. be 23 dollars, what is at 5 per cent be 10 dits, wat the time? Ans. 8 months. is the time! Ans. 1.Bri=lyr. 300. 2. Commission and Insurance. DEFINITIONS. 176. Commission is an allowance of so much per cent. to an agent for transacting business for another. Insurance is a contract by which certain persons, or companies, agree to make good losses of property by fire, storms, &c. in consideration of the payment to the insurer of so much per cent. on the value of the property insured. Premium is the sum paid by the owner of the property for the insurance. The written contract of insurance is called a policy. The policy should always cover a sum equal to the estimated value of the property insured, together with the premium; that is, a policy to secure the payment of 100 dollars at 2 per cent must be made out for 102 dollars. |