1. There are 17 boxes of sugar, each 1 cwt. 3 qrs. 18 lbs. gross, tare 16 lb. per cwt., trett 4 lbs. per 104 lbs.; what is the neat weight, and what is the value at $7.60 pr. cwt? 2. What is the neat weight and value of 12 bags of coffee, each 2 cwt. 1 qr. 10 lbs. gross, tare 18 lbs. per cwt., tret 4 lb. per 104 lbs. at $19.60 per cwt.? Ans. 22 cwt. 2 qrs. 18 lbs. cost $444.15. CASE V. When the tare is rated at so much per cent on the gross. RULE.-Multiply the gross by the tare per cwt. and divide by 100 for the tare, then calculate the amount as before. 1 1. What is the value of 15 hhds. of loaf sugar gross weight 68 cwt. 3 qrs. 21 lbs., tare 12 per cent. at 14 cts. per pound? Ans. $951.224. 2. What is the value of 4 hhds. of tobacco, weighing as follows: cwts. grs. lbs. No. 1 = 6 3 18 INTEREST. Q. What is the consideration or legal allowance for the use of money called? A. It is called interest or premium. Q. What is the sum lent called? A. The principal. Q. What is the legal interest or premium of $100 per annum called? A. The rate per cent. Q. Why is it called the rate per cent? A. Because, for a loan of $100, six dollars is allowed for its use for one year, it being considered the legal per centage in every State in the Union, except New York, in that state, the rate is $7 per annum. Time.-The number of years, months, or days for which interest is to be computed. Amount. The principal and interest added together is called the amount. GENERAL RULES AND THEOREMS FOR CALCULATING SIMPLE INTEREST IN DOLLARS AND CENTS. THEOREM I. This theorem is deduced from the principle, that any sum, at simple interest will double itself in 16 years, 8 months, or 200 months. Putting Pany given principal, T = any given time in months we have, RULE.-Multiply the given principal by half the given time in months, pointing off two figures on the right hand for decimals. THEOREM II. This theorem furnishes the shortest method possible for calculating simple interest for days: it is well known, that in banking institutions, interest is universally charged on all loans at the rate of one per cent. for sixty days. Therefore, it is manifest, that putting P = any given principle, and T any given time in days less than a = T year, we shall have 60: T :: 16 the interest of $100 for the given time. And again, = 6000 interest of P for the whole time. 6 RULE.-Multiply the principal by one-sixth of the given number of days, and divide their product by 1000, for cents, or point off 3 decimal places on the right hand, and you have the interest required. To find the interest of any sum for days. RULE.-Multiply the principal by of the days which denote as so many thousandths for decimals, the product when pointed will be the interest. By analysing, we find that as $100 gives $6 interest in 360 days, it will give a proportional interest for any other number of days, of which 360 is a multiple. Therefore, it will be clearly seen, that the interest of $100 for 60 days at 6 per cent. is $1.00; hence, it is manifest, that the interest for any given sum for 60 days, will be as many cents as there are dollars in the principal, for instance, the interest of 48 dollars for 60 days, is 48 cts. for $50 principal interest, 50 cents, and so on. 1. What is the interest of $80 for 60 days? 2. What is the interest of $90 for 60 days? 3. What is the interest of $40 for 60 days? 4. What is the interest of $45 for 60 days? Ans. 80c. 66 90c. 66 40c. 66 45c. CASE I. Equimultiples of sixty days. From the preceding illustration it is plain, that if the interest of 80 dollars for 60 days be 80 cents, the interest for 30 days will be 40 cents. 1. What is the interest of $240 for 120 days? Ans. $4.80. Illustration. The interest of $240 for 60 days would be 240 cents or $2.40, and as the ratio of 60 to 120 is as 1 to 2. Consequently, $2.40 x 2 = $4 80. 2. What is the interest of $300 for 120 days? Ans. $6.00. 3. What is the interest of 4. What is the interest of 350 for 120 days? 66 7.00. 66 9.20. METHOD OF CALCULATION IN BANKING INSTITUTIONS. RULE.-Multiply the principal by the number of days, including the days of grace, and the day on which the money was paid to the drawer, and divide by 60. 1. What is the interest (or bank discount,) on a note of $100 for 60 days. 6400 .60 + 4 = 64 × 100 = = 1063 or $1.07. 60 But the usual method of Bank calculation is more con cise; thus, $100 for 60 days, agreeably to the analysis of Theorem 2, is $1.00. 3 days grace + 1 day for payment. 4 days being toys of 60 is equal to .07 nearly, $1.07 as before. 2. What is the interest on a note of $100 for 90 days? Interest of $100 for 60 days is 100 for 30 days is Ans. $1.57. $1.00 0.50 .07 Interest for 3 days grace and day of payment, 3. What is the interest on a note of $100 for 116 Ans. $2.00. days? Operation.-116412060 × 2. The interest of $100 for 60 days is Multiply by $1.00 2 Answer, $2.00 ANOTHER METHOD. RULE. From the amount of the note, point of two figures to the right hand, this done, divide by 15, add the quotient to the principal, and the sum will be the interest required. 4. Calculate the interest on a note of $100 for 60 days? If for 90 days analyse it thus: for 60 ds. set down $1.07 5. Find the Bank interest on a note of $100 for 30 days? Ans. $0.57. 6. Find the Bank interest on a note of $240 for 90 days? Ans. $3.67. Note.-When no per centage is named, 6 per cent. is understood. CASE II. When the time is one year, and the rate per cent. any number of dollars. RULE.--If the principal be dollars, point out 2 places for cents. 2d. If it be in dollars and cents, point out 4 places for the decimal parts of a dollar. 3d. If in dollars, cents and mills, point out 5 places for the correct answer. |