1. What will be the interest on $1 for 5 months 6 days? ODD DAYS. 2. What is the interest of $1 for 13 months 16 days? The cents will be 6, and the mills 5, for the odd month, and 2 for 2 times 6 = 12 days, and there is a remainder of 4 days, the interest for which will be such part of 1 mill as 4 days is part of 6 days, that is, of a mill. Ans. '0673. 3. What will be the interest of $1 for 1 month 8 days? 2 months 7 days? 3 months 15 days? 5 months 11 days? months 22 days? 17 days? 4 6 mouths 8 months 11 days? 10 months 15 days? 7 months 3 days? 9 months 2 days? 11 months 4 days? 12 months 3 days? Note. If there is no odd month, and the number of days be Less than 6, so that there are no mills, it is evident, a cipher r ust be put in the place of mills; thus, in the last example, -12 months 3 days,-the cents will be '06, the mills 0, the 3 days a mill. Ans. '060 2 months 1 day? days? 4. What will be the interest of $1 for months 4 days? for 1 day? for 5 days? 10 months 5 days? for 2 days? 8 for 3 days? for 4 days? 5. What is the interest of $56'13 for 8 months 5 days? The interest of $1, for the given time, is '0408; therefore, ) and) $ 56'13 principal. 5 days '040% interest of $1 for the given time. 224520 interest for 8 months. 2806 interest for 3 days. 2'29197, Ans. $2291. 3 days + 2 days. As the multiplicand is taken once for every 6 days, for 3 days 'ake, for 2 days take 1, of the multiplicand. += §. So also, if the odd days be 4 2 days + 2 days, take of the multiplicand twice; for 1 day, take t Note. it the sum ou which interest is to be rast be less than $10, the mterest, for any number of days less than 6, will be less than 1 cent; consequently, in business, if the sum be less than $10, such days need not be regarded. From the illustrations now given, it is evident,-To find the interest of any sum in federal money, at 6 per cent., it is only necessary to multiply the principal by the interest of $1 for the given time, found as above directed, and written as a decimal fraction, remembering to point off as many places for decimals in the product as there are decimal places in both the factors counted together. EXAMPLES FOR PRACTICE. 6 What is the interest of $87'19 for 1 year 3 months? Ans. $6'539. 7. Interest of $116,08 for 11 mo. 19 days? $6'751. of $200 for 8 mo. 4 days? $8'132 of $0'73 for 10 mo. ? ( $'036. Note. The inte rest of $1 for 6 days being 1 mill, the dollars themselves ex press the interest in mills for six days, of which we may take parts. Thus, 6) 15000 mills, 2'500, that is, $2'50, Ans. to the last When the interest is required for a large number of years. it will be more convenient to find the interest for one year and multiply it by the number of years; after which find the interest for the months and days, if any, as usual. 18. What is the interest of $1000 for 120 years? Ans. $7200. 19. What is the interest of $520'04 for 30 years and 6 mouths! Ans. $951'673, 20. What is the interest on $400 for 10 years 3 months and 6 days? 50 years? Ans. $246'40. for 21. What is the interest of $220 for 5 years? 12 years? Ans. to last, $660. 22. What is the amount of $86, at interest 7 years? Ans. 122 12 23. What is the interest of 36 £. 9 s. 61 d. for 1 year? Reduce the shillings, pence, &c. to the decimal of a pound, by inspection, ( 76;) then proceed in all respects as in federal money. Having found the interest, reverse the operation, and reduce the three first decimals to shillings, &c., by inspection. (¶ 77.) Ans. 2 £. 3 s. 9 d. 24. Interest of 36 £. 10 s. for 18 mo. 20 days? Ans. 3 £. 8 s. 1 d. Interest of 95 £. for 9 mo.? Ans. 4 £. 5 s. 6 d 25. What is the amount of 18 £. 12 s. at interest 10 mouths 3 days? Ans. 19 £. 10 s. 94 d. 26. WL at is the amount of 100 £. for 8 years? Ans. 148 £. 27. What is the amount of 400 £. 10 s. for 18 months? Ans. 436 £. 10 s. 10 d. 3 q 28. What is the amount of 640 £. 8 s. at interest for 1 year? for 2 years 6 months? for 10 years? Ans. to last, 1024 £. 12 s. 91 d. ¶ 84. 1. What is the interest of 36 dollars for 8 months, at 4 per cent. ? Note. When the rate is any other than six per cent., first find the interest at 6 per cent., then divide the interest so found by such part as the interest, at the rate required, exceeds or falls short of the interest at 6 per cent., and the quotient added to, or subtracted from the interest at 6 per cent., as the case may be, will give the interest at the rate required. $36 '04 )144 36 1'08 Ans. 44 per cent. is of 6 per cent.; therefore, from the interest at 6 per cent. subtract 4 the remainder will be the interest at 44 per cent. 2. Interest of $54'81 for 18 mo., at 5 per ct.? Ans. $4'11. 3. ...... of $500 for 9 mo. 9 days, at 8 per ct.? $31'00. .....of $62'12 for 1 mo. 20 days, at 4 per ct.? $345. 5. Interest of $85 for 10 mo. 15 days, at 121 per cent.? Ans. $9'295. 6. What is the amount of $53 at 10 per ct. for 7 mo. ? Ans. $56'091. The time, rate per cent. and amount given, to find the principal. 85. 1. What sum of money, put at interest at 6 per cent., will amount to $61'02, in 1 year 4 months? The amount of $1, at the given rate and time, is $ 1'08 hence, $61'02 $1'08 56'50, the principal required; ÷ = that is, Find the amount of $1 at the given rate and time, by which divide the given amount; the quotient will be the princival required. Ans. $56'50. 2. What principal, at 8 per cent., in 1 year 6 months, will amount to $85'12? Ans. $76. 3. What principal, at 6 per cent., in 11 months 9 days, will amount to $99'311? Note. The interest of $1, for the given time, is '056; but, in these cases, when there are odd days, instead of writing the parts of a mill as a common fraction, it will be more convenient to write them as a decimal, thus, '0565; that is, extend the decimal to four places. Ans. $94 4. A factor receives $988 to lay out after deducting his commission of 4 per cent.; how much will remain to be laid out? It is evident, he ought not to receive commission on his own money. This question, therefore, in principle, does not differ from the preceding. Note. In questions like this, where no respect is had to time, (T 81, ex: 4, note,) add the rate to $1. Ans. $950. 5. A factor receives $1008 to lay out after deducting his commission of 5 per cent.; what does his commission amount to? Ans. $48. DISCOUNT. 6. Suppose I owe a man $397'50, to be paid in 1 year, without interest, and I wish to pay him now; how much ought I to pay him when the usual rate is 6 per cent. ? I ought to pay him such a sum as, put at interest, would, in 1 year, amount to $397'50. The question, therefore, does not differ from the preceding. Ans. $375. Note An allowance made for the payment of any sum of money before it becomes due, as in the last example, is called Discount. The sum which, put at interest, would, in the time and at the rate per cent. for which discount is to be made, amount to the given sum, or debt, is called the present worth. 7. What is the present worth of $834, payable in 1 year 7 months and 6 days, discounting at the rate of 7 per cent. ? Ans. $750. 8. What is the discount on $321'63, due 4 years hence, discounting at the rate of 6 per cent.? Ans. $62'26. 9. How much ready money must be paid for a note of $18, due 15 months hence, discounting at the rate of 6 per cent. ? Ans. $16'744. 10. Sold goods for $650, payable one half in 4 months, and the other half in 8 months; what must be discounted for present payment? Ans. $18'873 11. What is the present worth of $56'20, payable in 1 year 8 months, discounting at 6 per cent.? at 4 per cent.? at 5 per cent.? at 7 per cent.? at Ans. to the last, $48'869. The time, rate per cent., and interest being given, to find the principal. 86. 1. What sum of money, put at interest 16 months, will gain $10'50, at 6 per cent. ? $ 1, at the given rate and time, will gain '08; hence, $10'50 $'08 = $131'25, the principal required; that is,-Find the interest of $1, at the given rate and time, by which divide the given gain, or interest; the quotient will be the principal required. Ans. $131'25. 2. A man paid $4'52 interest, at the rate of 6 per cent. at the end of 1 year 4 months; what was the principal? Ans. $56'50. 3. A man received, for interest on a certain note, at the end of 1 year, $20; what was the principal, allowing the rate to have been 6 per cent.? Ans. $3333331. |