QUESTIONS FOR PRACTICE. 2. What is the amount of 10. What is the interest of $175.62 for 1 year and 6 £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 be .06 rate. .06 English money, the shillings, pence, &c. £5.190996 must be reduced to 10.5372 one yr. int. 1.5 the decimal of a 1.5 time. --- pound, (143.) then - The decimals 25954980 proceed as in Feder526860 below mills are 5190996 al money. The in -- terest will be 105372 omitted in the in | Ans.7.78649401 pounds and decimal --- answer to this parts, which must be reduced to Int. 15.80580 and the follow- | shillings, &c. (144) Pri. 175.62, ing questions. 11. What is the interest of f1 13s. 4d. for 1 year, at I Ans.191.425 amount. per cent. ? Ans. 3s. 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 and 10 days, at 6 per cent. | $240.16 for 3yr. 5mo. ld.? 73. Ans. $49.929. Ans. $49.272. 6. What is the interest of '15. What is the interest of $213.23 for 3 years and 12 958.54 for 5 days ? days, at 10 per cent. ? Ans. $0.793. Louis Ans. $67,079. 16. What is the interest of 7. What is the interest of $23.23 for 3 years, at 57 per. $1600 for 1 year and 3 months, I cent. ? at 6 per cent. ? Ans. $120. 51 per cept.=.055. 8. What is the interest of Ans. $3.832. $121.11, for 2 years and 7 17. What is the interest of months, at 5 per cent.?. £329 17s. 6d. 2qr. for 3 years, Ans. $15.643. 7 months, and 12 days, at 5 per cent ? £59 13s. 0 d. 9. What is the interest of 18. What is the interest of $124.18 for 2yr. 8 mo. ? $537.246 for 1 year at 6 per 'Ans. $19.868. 'cent? Ans. $32.234. 168, 169, 170. SIMPLE INTEREST. 415 SECOND METHOD. . ANALYSIS 168. 1. What is the interest of $60, for 5 months and 21 days, at 12 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 months 3 cents-and generally the number of months written as so many cents, or hundredths of a dollar, will be the interest for that time. And as the interest of 60. prin. for 1mo. (=30 days) is 1 cent, the interest for any .057 rate. number of days is so many 30ths of a cent, or 3ds of a inill. In the present example we write the 5 420 months as so many cents, or hundredths of a dollar, 300 and dividing the days by 3, find ļof them to be 7, which we write in the place of mills in the multi$3.420 Ans. plier ; and $60 multiplied by $0.057, (the interest of $1 for the given time, the product, $3.42, is evidently the interest of $60 for that time, 169. 2. What is the interest of $60 for 5 months and 21 days, at 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 2) 60. days written at the right hand. In the present exaniple half the months is 27, and if there were no odd days, we should write down 2cts. ' 5 mills, or 480 0.025 for the multiplier; but when there is an odd 120 month and days, as in the present case, it is as well 30 to call the odd month 30 days, and adding thereto the odd days, divide the whole by 6, the quotient (30+21 $1.710 Aps. :6=8]) will be mills. $0.028) then is the interest of $i for 5 mo. 21d. and 60 times $0.028), or $0.0284 times 60,(86)=$1.71 is the interest of $60 for the same time. To multiply 60 by, we take of 60, or divide 60 ty 2, and in general for the odd days, less than 6, we lake such part of the multiplicand 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, pro perly pointed, (122) will be the interest for the given time. · Note.-Odd days less than 6 are so many 6ths of a mill, and to multiply by these, proceed as follows : 190. ==={x} " " by 2 and 3 and add the quotient, or quotients, to the product of the principal by half the months. . 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. 020 .02, and as 6 is not con- 25 place of milis, that the and interest, July 29, 1823? -.- quotient, in dividing by lyr. mo. d. Ans. $585.583. An $1.525 3 may fall in its proper 1823 6 place. There being 3 decimal pla- | 29 ces in the factors, there must be 3 | 1020 0 22 pointed off in the product. 4. What is the interest of 1 2 10 7 Time. $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 in. ---- two first decimal places 1505 must be supplied with terest, was dated Feb. 14, 107 ciphers, and 7 must take i 1823; what was there due, ---- the place of mills. The principal and interest, Jan. 20, Ans. $1.612 use of the ciphers is to | 1824?. Ans. $29.092. guide us in pointing the product. 13. What is the amount of 5. What is the interest of | $87.91 on interest 3 years and $275.756, for 1 year, 9 months I 27 days ? Ans. $104.129. and 15 days ? Ans. $29.643. 6. Wliat 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. I Ans. $182.25. 7. What is the interest of l 15. What is the interest of $575 for 8 months ? $655 for 7 days? Ans. $23. Ans. $0.764. 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? Aps. $0.236. and 5 days ? Ans. $5.784. 171-174. SIMPLE INTEREST. 117 171. When the interest is any other than 6 per cent; first find the interest at 6 per cent. of which take such part as the interest required exceeds, or falls short, of 6 per cent, and this added to, or subtracted from, the 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 $5.98 for 2 years and 8 months, months, at 5 per cent. ? at 3 per cent.? Ans. $0.478. 165.45 principal. 19. What is the interest of 09 | $45 for 6 months. at 8 per · 6)14.8905 Int. at 6 per cent. cent.? Ans. $1.80. 2.4817 subtracted. i 20. What is the interest of $10.15 for 12 years, at 3 per Ans.$12.4088 Int at 5 per cent. cent. ? Ans. $3.654. VARIETIES IN SIMPLE INTEREST. 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, 1. The time, rate and amount being given, to find the principal. RULE.-Divide the given amount by 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 ! 3. What principal will amount 6 per cent. was $598; what was to $1700 in 1 year and 3 months at the principal ? Ans. $575. 1 5 per cent.? Ans. $1600. 173. 1. What principal will gain $1.35 in 9 months at 6 per cent. ? As $! in 9 months will gain $0.045, as many dollars will be required to gain $1.35 in 9 months, as the number of times 1.35 contains 0.045 and $1.35:-$0.045=830. Ans. Hence, i 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 rate, and the quotient will be the principal. 2. What principal will gain 23 | 3. What principal will gain 100 dolls. in 8 months ? Ans. $575. dolls. in 1 year and 3 months, at 5 i per cent. ?' Ans. 1600 dolls. 174. 1. If 30 dolls. gain 1 doll. 35 cents in 9 months, what is the rate per cent.? At l per cent for the given time, 30 dolls. will gain 22 cents 5 mills, the . rate therefore is so many times I per cent. as 22 cents 5 mills is contains ed in the whole gain, which is $1.35, i. e. $1.35=$0.2255.06, or 6 per cent. Ans. Hence, III. The principal, interest and time being given, to find the rate. RULE.—Divide the given interest by the interest on the given principal, at one per cent. for the given time, and the quotient will be the rate per cent. 2. If the interest on 573 dollars | 3. If the interest of 1600 dollars for 8 months be 23 dollars, what is for 1 year and 3 months, be 100 the rate per cent. ? dollars, what is the rate ? Ans. 6 percent. Ans. 5 per cent. 175. 1. If the interest on 30 dollars at 6 per cent. per annui, be 1 dollar and 35 cents, what is the time? The interest on 30 dollars for 1 year at 6 per cent. is 1 dollar and 80 cents. Now if the given interest be divided by the interest on the given principal for one year, the quotient will evidently be the number of years that principal was on interest-$1.35;$1.80-0.75yr.=4 months, (145) the answer. Therefore, IV. The principal, rate and interest being given, to find the time. RULE.--Divide the given interest by the interest of the given principal for 1 year at the given rate, and the quotient will be the time in years and decimal parts. 2. If the interest on 575 dollars 3. If the interest of 1600 dollars at 6 per cent. be 23 dollars, what is at 5 per cent. be 100 dollars, what the time? Ans. 8 months. is the time ? dos. 1.25yr.=lyr. 3mo. 2. Commission and \nsurance. 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. |