4. What is the interest of 6. What is the interest of £25 $175.62 for 1 year and 6 months, for 6 months, at 4 per cent ? at 6 per cent Ans. $15.805. Ans. 10s. 5. What is the interest of £1 7. What is the amount of 13s. 4d. for 1 year, at 9 per cent ? | $10.15 on interest 12 years at 6 Ans, 3s. Ans. $17.458. per cent : Case II. When there are years, months, and days in the time. RULE.*-Reduce the months and days to the decimal of a year; find the interest for 1 year by the preceding case, and multiply it by the years with the decimal annexed; the product will be the interest. Examples. 1. What is the interest of 2. What is the interest of $6.22 for 2 years, 6 months and $213.23 for 3 years and 12 days, 10 days, at 6 per cent? at 10 per cent? Ans. 864.679. =.5 6 3. What is the interest of --=.027 $1600 for 1 year and 3 months, 360 at 6 cent? Ans. $120. 6m. 10d.=.527 + 26124 7464 18660 4. What is the interest of 7464 $121.11 for 2 years and 7 months, at 5 per cent ? .9430764 or, Ans. $15.643. 94cts. 3m. Ans. 2.527 years. Case III. To cast the interest on any sum at 6 per cent. Rule.t-1. Under the principal write "half the even number of months, (with .5 at the right hand when there is an odd month) for a multiplier, by which multiply the principal and the product, after *Months are reduced to the decimal of a year by dividing them by 12, and days to the same decimal by dividing them by 360 ; which is considering the month 30 days, and the year 360, and is generally practised. If greater accu racy is required, find the number of days in the given months and days, and divide them by 365, the quotient will be the true decimal of a year. + This rule is a contraction of the Double Rule of Three. Any sum at 6 per cent. simple interest, doubles in 200 months ; hence we may say, if $100 removing the separatrix two figures from its natural place towards the left hand, will be the interest in dollars and parts of a dollar. 2. If there be days or an odd month and days in the given time, divide the days (calling the odd month 30) by 6, and place the quotient as a decimal on the right hand of half the even number of months, and proceed as before. 3. If the number of days be less than 6, supply the decimal place with a cipher, and divide the multiplicand according to the following table, and add the quotient to the product. Divide in the same manner, when there is a remainder after dividing the days by 6. Table. by 3. by 3 twice. by 2 and 3. by 2. mo. mo. in 200 months gain $100, what will a given principal gain in a given number of months ? EXAMPLE. -What is the interest of $300 for 8 months, at 6 per cent? $100 : 200m, :: $100 Here it will be seen that the three 300 : 8 first terms are invariable, and the 8 two last variable quantities ; and also that the first and third terms 2400 are equal, and therefore cancel each 100 other. Hence we discover that 200 is to any given principal as the num100x<200=20000)240000(12dolls. Ans. ber of months in the given time is 20000 to the interest. Take the foregoing example. Here it appears that the 40000 principal is multiplied by the whole 40000 number of months, and divided by 200 for the interest. Now let us divide the third term by the first, $ and multiply the second term by the 200 : 300 :: 8 quotient (8-2005.04 and $300> 8 .04512.) and the result is still the 20032400($12 Ans. as before. in the first tern, divide the third 200 term by 2, and multiply the second term by the quotient, cutting off the 400 two right hand figures of the product 400 8=2=4, and 300x4=1200) the result is still the same ; and this last is precisely the rule, for taking half the number of months is dividing by 2, and removing the separatrix in the product, makes the result the same as if the months had been divided by 200. By this rule, half the even number of months are so many units, one month is therefore ì, or .5, which is obtained by dividing 30 days by 6; and if any number of days less than 60 be divided by 6, the quotient may be considered a decimal of a unit, the value of which is 2 months, and may be found to any degree of exactness by annexing ciphers. But since by the rule we obtain only one decimal figure, if there is a remainder, it is necessary to take aliquot parts of the multiplicand for the odd days. Examples. 1. What is the interest of $275.756, for 1 year, 9 months and 15 days? 3 days= Div. 2)275.756 1 yr. 9mo.=21mo. and half the greatest even 10.7 number is 10, and Imo. 15ds.=45 days, which contain 6 seven times and 3 over. I therefore 1930292 write .7 at the right hand of 10 in the multi2757560 plier and for the 3 days, divide the multiplicand 137878 by 2. In the product I point off two more places for decimals than there are in the mulAns. $29.643770 tiplfcand and multiplier counted together. or $29.64cts. 3m. 2. What is the interest of 137 7. What is the amount of 212 dollars, 84 cents, for 2 years and dollars on interest for 14 months ? 6 months ? Ans. 20dls. 67cts.6m. Ans. 226 dolls. 84cts. 3. What is the interest of 575 dollars for 8 months ? Ans. 23 dollars. 8. A note for 27 dollars, 55cts. on interest was dated Feb. 14, 4. What is the interest of 13 1823; what was there due, prindolls. 41cts. for 3 months and 16 days? Ans. 23cts. 6m. cipal and interest, Jan. 20, 1824 ? Ans. 29dolls. 9cts. 2m. 5. What is the interest of 49 dollars, 25 cents for 3 years, 3 months and 3 days ? 9. What is the amount of 87 Ans. Idolls. 62cts. 8m. dollars, 91 cents on interest 3 6. A note for 500 dollars on years and 27 days ? interest, was dated Sept. 22,1820, Ans. 104dolls. 12cts. 9m. what was due, principal and interest, July 29, 1823 ? yr. mo. d. Ans. $585.583. 10. What is the interest of 1823 6 29 607 dolls. 50cts. for 5 years ? 1820 8 22 Ans. 182dolls. 25cts. To find the interest for short periods of time, at six per cent. Rule.* -Multiply the principal by the time in days, (calling each year 360, and each month 30 days,) and divide the product by 6; * This will be found a very convenient practical rule for casting interest for short periods of time, and it is easily remembered. The invention of the rule is similar to the preceding, dividing by 6 and removing the separatrix three figures towards the left hand, being the same as dividing by 6000 days, the number in 200 months, of 30 days each. the quotient, after removing the separatrix three figures from its natural place towards the left hand, is the interest in dollars and parts of a dollar. Examples. 1. What is the interest of 17 dollars, 68 cents for 11 months and 28 days? 17.68 30 358 Here the separatrix naturally falls between 4 and 4; I therefore count off 1444 three more figures towards the left hand, 28 8840 and place the point between 1 and 0, 5304 and the answer is 1 dollar, 5 cts. 4m. 11 mo 330 days 358 days. 6)6329.44 $1.05440 Ans. 2. What is the interest of 215 dolls. for 1 month and 14 days? Ans. Idoll. 57cts. 6m. 4. What the interest of 76 dolls. 25cts. 6ni, for 1 year, 3 months and 5 days? Ans. 85.782. 3mo.= 90 5 lyr.=360 3. What is the interest of 655 dolls. for 7 days? Ans. 76cts. 4m. 455 days. When the interest is any other than 6 per cent; first find the interest at 6 per cent. by Case III. or 1V. of which take aliquot parts and add to, or subtract from the interest at 6 per cent. as the case may require. Examples. 1. What is the interest of 165. 2. What is the interest of 5 dolls. 45cts. for 1 year and 6mos. dolls. 93cts. for 2 years and 8 at 5 per cent! months, at 3 per cent ? 165.45 principal. Ans, 47 cts. 4m. 9 3. What is the interest of 45 6)14.8905 Int. at 6 per cent. dolls. for 6 months, at 8 per cent ? 2.4817 subtracted. Ans. 1doll. 80cts. Ans. $12.4088 Int. at 5 per cent. Case V. To find the interest of any sum by decimals. RULE.-Multiply the principal by the ratio, and that product by the time ; the last product will be the interest required. Note. The ratio is the simple interest of $1 for 1 year at the rate agreed on, thus At 3 per cent. the ratio is .03 is .04 is .05 At 51 is .055 is .06 is .065 is .07 At 5 16 At 6 « At 8 66 Examples. 1. What is the interest of 823 2. What is the interest of 23cts. for 3 years at 54 per cent? 8223.14 for 5 years, at 6 per 23.23 cent? Ans. 866.942. .055 ratio. 3. What is the interest of 11615 $10.15 for 12 years, at 3 per 11615 cent? $3.654. 1.27765 3 time. 4. What is the amount of 123 cents, for 500 years, at 6 per cent? Ans. 83.875. $3.83295 Ans. Case VI. To compute interest on Notes, Bonds, g'c. PRINCIPLES.*-1. If the contract be for the payment of interest annually, the interest becomes due at the end of each year, and if it * These are the principles on which interest is allowed by the courts of law in Vermont. The following methods are sometimes practised in casting the interest on notes, &c. 1. Find the amount of the principal for the whole time, and also the amount of the endorsemenls from the time they were made ; deduct the later from the former, and the remainder will be the sum due. But this method would be unjust ; for, suppose a note be given for $100 with interest, and $6 be paid at the end of each year for 4 years, which is endorsed on the note. Now the interest of the principal for this time is $24, just equal to the sum of the payments; but by this method the several payments all draw interest from the times they are made, the first 3 years, the second 2, and the third 1,= 1 08+.72+ 363 $2.16, which goes towards paying the principal, and in this way any debt would in time be extinguished by the payment of the interest annually. 2. Cast the interest up lo the first payment, and if the payment exceed the interest, deduct the excess from the principal, and cast the interest on the remainder up to the second paynient, and so on. If the payment be less than the inteest, place it by itself, and cast the interest up lo the next payment, and so on lill the payments exceed the interests, then deduct the excess from the principal, and proceed as before. By this method the interest is supposed to be always due at the time the payment is made. The impropriety of this, as a general rule, may be shown by an example. Supposing A has a note against B for $10000 with interest, payable in one year, and B pays $200 at the end of every 2 |