What is the duty, at 30 per cts. per lb. ? gross 13791 lb., tare 2 per cent.? 13 cwt. 3 qr. hemp, valued 108. INTEREST. Interest is a certain percentage of a sum of money paid by the borrower to the lender for the use of it. Principal is the money lent, or on which the interest is to be paid. Rate is a certain per cent. agreed upon. It is generally fixed by law at 6 per cent. per annum. Amount is the principal and interest added together. NOTE. In the following questions in interest, the annual rate is understood to be 6 per cent. unless some other rate is named. 1. What is the interest of $1 for 1 yr. at 6 per cent.? $10? $15? $35? 2. What is the interest of $15 for 1 year? 2 years? 3 years? 5 years? 3. What is the interest of $18 for 1 year? For 2 months: = tyr.? 3 mo.? 6 mo. ? 4. What is the interest of $12 for 1 yr. 2 mo. = 1 3 mo. = 1 yr.? 1 yr. 6 mo. ? 1 yr. 4 mo.? 2 yr.? $20 for 2 yr. 4 mo.? 2 yr. 1 mo.? 3 yr. 6 mo. ? 5. What is the interest of $30 for 1 yr. at 5 per cent.? 3 mo.? 1 yr. 6 mo.? yr. yr.? 2 yr. 2 mo.? For 1 yr. 6. What is the interest of $6 for 1 yr. at 7 per cent.? For 1 yr. 2 mo.? 2 yr. 4 mo. ? If the rate of interest is 6 per cent. per annum, for 2 months it will bet of 6 per cent., or 1 per cent., of the principal. 7. What is the interest of $1 for 2 mo.? How much for 1 mo. ? Ans. of a cent, or 5 mills. For 3 months? Ans. 1 cent, or 1 cent 5 mills. For 4 mo.? 5 mo.? 6 mo.? 7 mo.? 8 mo.? 9 mo.? 1 yr. 3 mo. 15 mo. ? Since 6 days are of 60 days, or 2 months, if the interest of $1 for 2 months is 1 cent, for 6 days it will be of 1 cent, or 1 mill; for 12 days, 2 mills, &c. 8. What is the interest of $1 for 6 days? 1 day? Ans. of a mill? 24 days? 18 days? For 5 days? Ans. § of 1 mill. For 8 days? Ans. 1 mill. For 12 days? 17 days? 27 days? Hence, To find the interest of $1 for any given time, when the rate per annum is 6 per cent., RULE 1. Reduce the years and months to months, and call the number of months cents, and ↓ of the number of days mills. 9. What is the interest of $1 for 2 months and 12 days? Ans. $0.012. For 3 mo. 18 da.? Åns. $0.018. Why? Ans. $0,042. For 7 mo. 16 d.? Ans. For 8 mo. 15 d.? $0.0373. 10. What is the interest of $1 for 9 mo. 25 d.? For 1 yr. 3 mo. 28 d. = = 15 mo. 28 d.? For 3 9 mo. ? 11. For 5 yr. 7 mo. 23 d.? 3 yr. 11 mo. 29 d. ? 1 mo. 21 d. ? yr. 4 yr. To find the interest on any given principal, at 6 per cent., RULE 2. Find the interest of $1 for the given time by the last rule, and multiply the interest thus found by the given principal. 12. Compute the interest on $561.14 for 2 yr. 7 mo. 20 d. NOTE. The interest of $1 for 31 mo. is $0.155; for 20 da. it is $0.0031, which, being added, gives $0.158). Multiplying this by the principal gives the interest on $561.14. Ans. $88.847. 3 13. Find the interest on $48.17, for 1 yr. 3 mo. 8 d; for yr. 7 mo. 12 d.; 4 yr. 8 mo. 9 d.; for 5 yr. 7 mo. 27 d. 14. What is the interest on $1418.46, from Jan. 15, 1841, to Nov. 25, 1846? (69.) from Dec. 14, 1845, to May 6, 1848? from July 4, 1776, to March 23, 1781? from Aug. 25, 1837, to Nov. 7, 1848? 15. What is the amount of $2007.81, from Feb. 21, 1844, to Jan. 15, 1849? from Oct. 17, 1832, to April 12, 1850? from Nov. 25, 1845, to Jan. 20, 1849? To compute the interest when the rate per annum is either more or less than 6 per cent., RULE 3. Having found the interest at 6 per cent. by Rule 2, make a proportional addition or subtraction; for 7 per cent. add; for 5 per cent. subtract ; for 5 per cent. subtract ; for 7 per cent. add 1, &c. Take the 12th example. The interest at 6 per cent. is $88.847; at 7 per cent. it would be 103.656; at 51 per cent., $81.443. 16. What is the interest of $48.17, for 1 yr. 3 mo. 8 d., at 5 per cent.? at 4 per cent.? 7 per cent.? 7 per cent.? 9 per cent.? 121 per cent.? 34 per cent.? 17. Compute the interest on $35.125, at 61 per cent., for 3 mo. 15 d.; at 7 per cent., for 1 yr. 5 mo. 20 d.; at 63 per cent., for 8 yr. 9 mo. 15 d.; at 52 per cent., for 3 yr. 4 mo. 24 d. Some practical men prefer to compute interest by the following rule. It is not commonly so short a method as that before given, but as it is sometimes desirable to compute the interest by different methods, in order to test the correctness of a result, the pupil should learn to compute interest by it. RULE. Multiply the principal by the rate per annum, expressed decimally (102); the product will be the interest for 1 year. From this, calculate the interest for any number of years, months or days, as in Practice. (100.) NOTE. The pupil may do the following questions by both methods. 18. What is the interest of $416, for 1 year, at 6 per cent.? at 5 per cent.? at 6 per cent.? at 7 per cent.? at 8 per cent.? 19. What is the interest on $517.84, for-1 yr. 5 mỏ. 12 d., at 7 per cent. ? 20. What will $52.87 amount to in 8 mo. 27 d., at 7 per cent.? 21. What is the interest of $461.75, at 51 per cent., for 2 years? for 2 yr. 3 mo.? for 3 yr. 4 mo.? mo. ? for 4 yr. 5 22. What is the interest of $923.50, at 41 per cent., for 5 years 6 mo.? for 6 yr. 7 mo.? for 7 yr. 8 mo. ? 23. What is the interest of $1385.25, for 6 yr. 9 mo., at 7 per cent.? for 7 yr. 10 mo.? for 9 yr. 11 mo.? 24. Compute the interest on $35.125, at 6 per cent., for 3 mo. 15 d.; 8 mo. 24 d.; 1 yr. 5 mo. 20 d. yr. 25. What is the amount of $70.25, at 6 per cent., for 3 2 mo. 27 d.; for 8 yr. 9 mo. 15 d., at 7 per cent.; for 3 yr. 4 mo. 24 d., at 51 per cent.? To find the interest on pounds, shillings, pence, &c., for any given time, RULE. Reduce the shillings, &c., to the decimal of a pound (86); annex it to the pounds, and then multiply by that decimal of a £ which expresses the interest of £1 for the given time, and reduce the decimal in the result to shillings, pence, &c. NOTE. Shillings, pence and farthings, may be reduced to the decimal of a pound by the following RULE. Write half the shillings as tenths, and if there is an odd shilling, call it 5 thousandths; write the farthings in the given pence and farthings as so many thousandths, increasing their number by 1 when it exceeds 12, and by 2 when it exceeds 36; and add the numbers. 26. What is the interest of £54 17s. 94d., for 1 15 d., at 6 per cent.? Solution. 17s.£.85; 91d.£.040; .85+.040-£.89. £54 17s. 91d.=£54.89 .087 rate per cent. for 1 yr. 5 mo. 15 d. 38423 43912 2744 £4.80287=£4 16s. Od. 2.7 qr., the answer. 27. Find the interest, at 6 per cent. per annum, of £150 6s. for 8 mo. 15 d.; of £75 15s. 6d. for 3 mo. 18 d. ; of £950 19s. 73d. for 3 yr. 7 mo. 25 d.; of £105 Os. 94d. for 1 mo. 14 d., at 4 per cent. per annum. NOTE. Get the shillings, &c., to the nearest thousandths of a £, and the answer to the nearest qr. 109. PARTIAL PAYMENTS. LEGAL RULE. When partial payments have been made and endorsed on notes or bonds, the following is the rule adopted by the United States courts, and most other courts, for computing the in terest. LEGAL RULE FOR PARTIAL PAYMENTS. 1. Compute the interest on the given principal up to the time of the first payment, and if it is less than the payment, add it to the principal. From this amount subtract the first payment; the remainder will be a new principal. 2. Compute the interest on this new principal from the time of the first payment to the time of the second payment, and if it is less than the payment, subtract the second payment from the amount, for another new principal, as before, and thus proceed till the time of settlement. 3. If any payment is less than the interest due at the time the payment is made, subtract the payment from the interest, (not from the amount,) and add the excess to the next interest, to be computed on the same principal as before, to the time of the next payment; so THAT NO NEW PRINCIPAL SHALL BE GREATER THAN THE PRECEDING ONE; as in the following example. NOTE. Merchants and bankers usually reject mills in their computations; but when the fraction of a cent is or more, they add one to the number of cents. The pupil may do so in the next nine articles. |