per cent. of months, by the principal, for the interest at 6 per cent. according to Rule, 2nd case. 1. What is the interest of $65 for 3 years, 4 months, at 6 per Ans. $13.00. 2. What is the interest of $199.11 for 3 years 8 months at 6 per cent? Ans. $43.80.4. 3. What is the interest of $98 for 4 years 2 months? Ans. $24.50. 4. What is the interest of $1298.40 for 4 years 8 months? Ans. $363.55.2. CASE VI. To find the Interest of any given principal for any num ber of years, months and days, at six per ct. per annum. RULE.-Bring the years and months to months, take one-sixth of the days, which annex to half the months, multiply that number by the principal, and point out three decimal places in the product. One for mills and two for cents, which will give the correct answer. It may be asked, why we take ţ of the days, an answer is at hand; because, 30 days is the general average of a month;-Days are therefore, thirtieths of a month, and sixtieths of half months, because the Interest of any sum at 6 per cent. is exactly i per cent. a month.--Hence if t of the days be taken they will become tenths, or decimals of a month. 1. What is the interest of $400 for 3 years, 4 months and 12 days, at 6 per cent. per annum? $80.80. yrs. m. d. Illustration, 3 4 %)12 12 2 1)40 202 80.80.0 Answers 2. Calculate the interest of $360 for 2 years 8 months and 18 days. Ans. $58.68. 3. Calculate the interest of $800 for 1 year 8 months and 6 days? Ans. $80.80. 4. Calculate the interest of $240.65 for 4 years, 4 months and 15 days? Ans. $63.17. 5. Calculate the interest of $67.50 for 1 year, 7 months and 7 days? $6.49 6. Calculate the interest of $23.19 for 2 years, 5 months and 11 days? $3:40.5. CASE VII. When the Interest is required from a certain day of the month, in a year, to a particular day of the month in the same or in, another year. 1. What is the interest of $30, from Feb. 6th, 1838, up to June 22d, 1840? Ans. $4.28. 2. What is the interest of $35.61 from Nov. 11th, 1831, up to Dec. 15th 1833? Ans. $4.47.4. 3. What is the interest of $11.101, from April 17th, to Dec. 7th, 1832, at 7 per cent.? Ans. $0.49.6. 4. What is the interest of $369.29, from April 30th 1830, to July 31st 1832, at 4 per cent.? Ans. $33.28. 5. What is the interest of $1728.75, from Nov. 19, 1823, up to June 18th, 1826? Ans. $267.66.8. 6. What is the interest of $99.99.9, from Jan. 1st, 1800, to Feb'y 29th, 1832? Ans. $192.96.4. PARTIAL PAYMENTS ON BILLS AT INTEREST. In the Supreme Court of the United States, and, indeed, in most courts of the several States, the following rule is generally adopted, for estimating interest on Notes and Bonds; when partial payments have been made. GENERAL RULE. Compute the interest on the principal sum, from the time when the interest commenced, to the first time when a payment was made, add that interest to the principal, and from the sum subtract the payment made at that time, together with the preceding payments, if any, and the remainder forms a new principal; on which compute and subtract the interest, as upon the first principal, and proceed in the same manner to the time of judgment. Wilmington, Del. June 17, 1829. For value received, I promise to pay Joseph Miller, or order, on demand, seven hundred and sixty-nine dollars, and eighty-seven cents, with interest. $769.87. NELSON CLELAND. Ans. $211.92. yrs. m. d diff. of time. 0 8 15 payment, $802.59 75.50 1 Balance for new principal, $727.09 m. d. 55.74 782.83 Subtract second payment, . 165.00 Balance for new principal, $617.83 diff. of time. diff. of time. 0 3 4 $627.51 Subtract third payment, 171.00 Balance for new principal, $456.51 yrs. d. 1832 1 21 1831 9 15 Int. for 3m. 6d. 7.30 m. diff. of time. 0 3 6 $463.81 Subtract fourth payment, 47.25 Balance for new principal, $416.56 yrs. m. d. 1833 3 5 $416.56 1832 1 21 Int. for ly. 1m. 15d. 28.12 1 1 15 $444.68 Subtract fifth payment, 12.17 Balance for new principal, $432.51 yrs. d. 1833 12 6 1833 3 5 Int. for 9m. 1d. 19.54 diff. of time m. Miff. of time. 0 9 1 $452.05 Subtract sixth payment, 98.00 Balance for new principal, $354.05 yrs. d. 1834 7 7 1833 -12 6 Int. for Oy. 7m. 1d. 12.45 m. diff. of time. 0 7 1 $366.50 169.00 m. Balance for new principal, $197.50 yrs. d. 1835 9 25 1834 7 7 diff. of time. 1 2 18 Int. for ly. 2m. 18d. 14.42 Due on the 25th September, 1835, $211.92 Baltimore, March 10, 1840. For value received I promise to pay Simon Kemp, fifty four dollars and eighteen cents, with interest. $54.18. JAMES HOOPER. Attest, John E. STANSBURY. On this note are the following payments: June 10, 1840, received twelve dollars and twenty-five cents. August 16, 1840, received ten dollars. October 21, 1840, received twenty dollars. March 4, 1841, received five dollars. What sum will be due on the 4th day of July, 1841? Ans. $9.04. MISCELLANEOUS QUESTIONS IN INTEREST. CASE I. Principal interest and time given to find the rate per cent. 1. At what rate per cent. must $500 be put on interest to gain $120 in 4 years? RULE.—Multiply the interest by the time, and subtract the product from the amount, the remainder will be the interest gained at 1 per cent. for the given time, provided the difference be less than the principal, divide the interest by that remainder, and the quotient will be the rate per cent. required. Illustration. - 120 x 4 480, 500 — 480 = 20, and * = 6 per cent as required. Proof.-$500 at 6 per cent per annum gives $30 interest, which being multiplied by 4, $120 the interest of $500 for 4 years. 2. If I receive $60 interest for the use of $600, 1 year, 8 months, what is the rate per cent. Ans. 6 pr.ct. 3. If I pay $200 for the use of $2000, for 2 years 6 months, what is the rate per cent? Ans. 4 per ct. 4. At what rate per cent. must $400 be put to interest to gain $120 in 5 years? Ans. 6 per ct. 5. At what rate per cent. must $500 be put on interest to gain $120, in 4 years? Ans. 6 per ct. |