: UTICA, May 1, 1836. 2. For value received, I promise to pay Isaac Spencer Clark, or order, three hundred and forty-nine dollars ninety-nine cents and eight mills, with interest, at 6 per cent. JAMES N. BROWN. Endorsements were made on this note as follows: Dec. 25, 1836, there was paid $49.998 June 30, 1837, 6 " " . 4.998 Aug. 22, 1838, 66 66 15.000 June 4, 1839, " " " . 99.999 How much was due April 5, 1840 ? The amount of the note, or principal, is $349.998 Interest up to Dec, 25, 1836, is 13.650 19.993 This sum is still less than the interest now due. Endorsement June 4, 1839, 99.999 $119.997 This sum exceeds the interest now due. 239.603 12.020 Interest up to April 5, 1840, is 251.623 UTICA, Dec. 9, 1835. 3. For value received, I promise to pay Peter Smith, or order, one hundred and eight dollars and forty-three cents, on demand, with interest, at 7 per cent. JOHN SAVEALL. Endorsements were made as follows: March 3, 1836, there was endorsed $50.04 Dec. 10, 1836, “ “ 13.19 May 1, 1838, 66 66 66 50.11 How much remained due Oct. 9, 1840 ? Ans. $5.844. UTICA, Aug. 1, 1837. 4. For value received, I promise to pay W.Frederick Gould, or bearer, one hundred and forty-three dollars and fifty cents, on demand, with interest. . DUDLEY FARLING. Dec. 17, 1837, there was endorsed $37.40 17.09 13.13 Sept. 9, 1840, 666 66 50.50 How much remains due Dec. 28, 1840, the interest being 7 per cent. ? 5. A note of $486 is dated Sept. 7, 1831, on which, March 22, 1832, there was paid $125 Nov. 29, 1832, " " " 150 May 13, 1833, " 16 " What was the balance due April 19, 1834, the interest be. ing 7 per cent. ? 120 67. The principal, the rate per cent., the time, and the interest, are so related to each other, that any three of them being given, the remaining one can be found. PROBLEM I. Given the principal, the rate per cent., and the time, to find the interest. The rule for this problem has already been given under case III. Art. 65; it is as follows: RULE. Multiply the interest of $1, for the given time, and given rate per cent., by the principal. PROBLEM II. Given the time, the rate per cent., and the interest, to find the principal. By the reverse of the last problem we obtain this ' RULE. Divide the given interest by the interest of $1, for the given time, and given rate per cent. Examples. 1. The interest on a certain principal, for 9 months and 10 days, at 41 per cent., is $1.01605. What was the principal? In this example we find the interest of $1, for 9 months 10 days, at 41 per cent., to be $0.035; .. $1.01605, divided by $0.035, gives $29.03, for the principal required. 2. What principal will, in 1 year 7 months and 15 days, at 6 per cent., give $9.75 interest ? Ans. $100. 3. What principal will, in 7 years and 9 days, at 6 per cent., give $16.86 interest? Ans. $40. 4. What principal will, in 3 years and 6 months, at 5 per cent., give $92.75 interest ? 5. What principal will, in 3 months and 9 days, at 8 per cent., give $90 interest? PROBLEM III. Given the principal, the time, and the interest, to find the rate per cent. . RULE. Divide the given interest by the interest of the given principal, for the given time, at 1 per cent. Examples. 1. The interest of $100, for 9 months and 10 days, is $3.50. What is the rate per cent. ? In this example we find the interest of $100, for 9 months and 10 days, at 6 per cent., to be $4.665. The interest at 1 per cent. is $0.77%; therefore, dividing $3.50 by $0.77), we obtain 4, for the rate per cent. required. 2. At what rate per cent. will $530, in 3 years and 6 months, give $92.75 interest? Ans. 5 per cent. 3. At what rate per cent. will $19.41, in 1 year 7 months and 13 days, give $2.2003392 interest ? Ans. 7 per cent. 4. At what rate per cent. will $5.37, in 4 years 12 days, give $1.73272 interest ? 5. At what rate per cent. will $4070, in 3 months, give $91.575 interest ? PROBLEM IV. Given the principal, the rate per cent., and the interest, to find the time. RULE. Divide the given interest by the interest of the given princi. pal, for 1 year, at the given rate per cent. Examples. 1. In what time will $37.13, at 4° per cent., give $0.7518825 interest? In this example we find the interest of $37.13, for 1 year, at 41 per cent., to be $1.67085; .'. dividing $0.7518825 by $1.67085, we get 0.45 years; this, reduced to months and days, gives 5 months and 12 days. 2. In what time will $700, at 7 per cent., give $85.75 in. terest ? Ans. 1 year 9 months. 3. In what time will $100, at 6 per cent., give $100 interest ? That is, in what time will a given principal double itself at 6 per cent. interest ? Ans. 164 years. 4. In what time will a given principal double itself ato per cent. ? Ans. 144 years. - 5. In what time will a given principal double itself at 8 per cent. ? Ans. 121 years. 6. In what time will a given principal double itself at 5 per cent. ? 17. In what time will a given principal double itself at 45 per cent. ? The following table gives the time required for a given principal to double itself at simple interest. |