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 year, we shall have 60: T : : 1 = 66 = the interest of = $100 for the given time. And again, T T T X P P interest of P for the whole time. 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 × 2 = $4.80. 2. What is the interest of $300 for 120 days? Ans. $6.00. 3. What is the interest of 350 for 120 days? 66 7.00. 4. What is the interest of 460 for 120 days? (6 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 = 1 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 to 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 Ans. $1.57. $1.00 0.50 .07 $1.57 100 for 30 days is Interest for 3 days grace and day of payment, viz: 4 days is 3. What is the interest on days? a note of $100 for 116 Ans. $2.00. Operation.-1164 120 60 × 2. The interest of $100 for 60 days is $1.00 Multiply by 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. 1. What is the amount of $144 for 1 year at 6 per Amount, $152.64 2. What is the amount of $240.75 for one year at 6 per cent? Ans. $255.191⁄2. 66 1.22. 97.20, 3. What is the interest of $640 for 1 year? Ans. $38.40. 4. What is the interest of $20.33, “ 5. What is the interest of $1620 (6 6. What is the interest of $19.64 for 2 years? 66 Ans. $2.36 nearly. To find the interest for years and months. CASE III. Bring the years to months, and multiply the principal by the number of months, and half the product will be the interest, or take half the months and multiply it by the principal. 1. What is the interest of $325 for 12 years? Ans. $234.00. 2. What is the interest of $617.56 for 25 years? Ans. $926.34. 3. What is the interest of $17,696.56 for 10 years? Ans. $10,617.93. 4. What is the interest of $250 for 11 years? Ans. $165.00. 5. What is the interest of $13.93 for 3 years? Ans. $2.50. To find the interest for months at six per cent. RULE.-Multiply the principal by half the number of months, and proceed as before. 1. Find the interest of $240.75 for 2 months at 6 per cent per annum? Ans. $2.403. 2. Find the interest of $320.25 for 3 months? Ans. $4.80.3 + 3. Find the interest of $480.90 for 4 months? Ans. $9.61.8. 4. Find the interest of $325.92 for 5 months? Ans. $8.14.8. 5. What is the amount of $240.92 for 2 years, 10 months at 7 per cent.? Ans. $288.70.2. 6. What is the amount of $325.15 for 3 years, 5 months, at 5 per cent.? Ans. $380.70. CASE IV. When the rate of Interest is at any per centage more or less than six per cent. RULE. Find the Interest of the given PRINCIPAL at 6 per cent., as before directed; then multiply that interest by the given rate per cent. more or less than 6 per cent. and divide the product by 6, and you get the interest required. 1. Calculate the interest on a note of $275 for 4 months at 7 per cent.? Ans. $6.41. 2. Calculate the interest of $350 for 5 months, at 5 per cent.? Ans. $7.29 + 3. Calculate the interest of $248.75 for 11 months, at 7 per cent.? 4. Calculate the interest of $365.67 for 7 months, at 3 per cent.? Ans. $6.40. 5. Calculate the interest of $600 for 15 months at 5 per cent.? Ans. $37.50. Ans. $15.96. 6. Calculate the interest of $90.80 for 19 months, at 6 per cent. per annum? Ans. $8.62.6. CASE V. When the Interest is required for any number of years and months. RULE.-Bring the years and months, to months, take half the sum; multiply that half sum, or half the number |