number of cents: and for the time more or less than 60 take aliquot parts. * EXAMPLES. 1. What is the interest of 1542 dollars for 90 days, at 6 per cent. per annum? also, for 60,† for 30, and for 20 days, at the same rate? per cent. per annum? dollars for 90 days, at Ans. $11.562. 3. What is the interest of 3084 dollars for 30 days, at 6 per cent. per annum? 6 Ans. $15.42. 4. What is the interest of 2324 dollars for 54 days, at per cent. per annum? Ans. $20.91. + 5. What is the interest of 3942 dollars for 50 days, at 6 per cent. per annum? Ans. $32.85. CASE 5. To find the principal, when the amount, time, and rate per cent. are given. RULE. Find the amount of 100 pounds, or dollars, at the rate and time given: then, 1 As the amount of 100 pounds, or dollars, Is to the amount given, So are 100 pounds, or dollars, To the principal required. *This is calculating after the rate of 360 instead of 365 days to the year, which will always make the interest rather too much. If the interest found by this rule be divided by 73, the quotient will show by how much it exceeds the true interest. + When a note is drawn for 60 days, the interest is mostly calcu lated for 63, on account of three days, called days of grace, which are commonly allowed the payer, on all notes, after the time expires for which they were drawn. The interest is here only computed for the given time. EXAMPLES. 1. What principal at interest for five years, at 6 cent. per annum, will amount to 650L.? per Ans. 500L. 2. What principal at interest for 10 years, at 6 per cent. per annum, will amount to 1300L.? Ans. 812L. 10s. 3. What principal at interest for 4 years, at 5 per cent. per annum, will amount to $571.20? CASE 6. Ans. 476 dollars. To find the rate per cent. when the amount, time and principal are given. RULE. Subtract the principal from the amount, and the remainder will be the interest for the given time: then, As the principal, Is to one hundred pounds or dollars, So is the interest of the principal, for the given time, To the interest of 100 pounds, or dollars, for the same time: 1. At what rate per cent. per annum, will 500L. amount to 650L. in 5 years? Ans. 6L. per cent. 109 INSURANCE, COMMISSION, AND BROKAGE. 2. At what rate per cent. per annum, will 500L. amount to 725L. in 9 years? Ans. 5L. per cent. 3. At what rate per cent. per annum, will 600 dollars amount to 856 dols. 50 cts. in 9 years and 6 months? Ans. 4 per cent. CASE 7. To find the time, when the principal, amount, and rate per cent. are given. RULE. Find the interest of the principal for one year. Find the interest for the time required, by subtracting the principal from the amount: then, As the interest of the principal for one year, So is one year, To the time required. EXAMPLES. 1. In what time will 500L. amount to 725L. at 5 per Ans. 9 years. L. 25 00 225 Interest for time required. 2. In what time will 540L. amount to 734L. 8s. at 4 per cent. per annum? · Ans. 9 years. 3. In what time will 600 dollars amount to 798 dollars, at 6 per cent. per annum? Ans. 5 years. INSURANCE, COMMISSION, AND Insurance, Commission, and Brokage, are allowances made to insurers, factors, and brokers, at a stipulated rate per cent. RULE. Work as if to find the interest of the given sum for one year, at the proposed rate: or, if the rate be less 110 INSURANCE, COMMISSION, AND BROKAGE. than 1 per cent. take such aliquot part, or parts, of the interest at 1 per cent. as the rate is of a pound, or dollar. EXAMPLES. 1. What is the commission on 596L. 18s. 4d. at 6 per cent.? Ans. 35L. 16s. 3 d. L. S. d. 596 18 4 6 L. 35 81 10 0 s. 16/30 12 d. 3160 qr. 2/40 2. What is the commission on 1371L. 9s. 5d. at 5 Ans. 68L. 11s. 5d. per cent. ? 3. What is the commission on 526L. 11s. 5d. at 34L. Ans. 18L. 8s. 7d. per cent.? 4. What is the commission on 1974 dollars, at 5 dollars per cent.? Ans. $98.70. 5. A factor has sold goods for a merchant, to the amount of 930L. 10s. and is to receive 34L. per cent. commission: what sum is due to him? Ans. 30L. 4s. 9 d. 6. What is the insurance of 924L. at 7L. per cent.? Ans. 64L. 13s. 7d. 7. What is the insurance of 1250 dollars, at 71⁄2 dollars per cent.? Ans. $93.75. 8. What is the insurance of an East India ship and cargo, valued at 14813L. 15s. at 15 L. per cent.? Ans. 2333L. 3s. 34d. 9. What is the brokage on 1321L. 11s. 4d. at 1L. per cent.? Ans. 14L. 17s. 4d. 10. What is the brokage on 874L. 15s. 3d. at 5s. or 4L. per cent.? Ans. 2L. 3s. 8 d. 11. If a broker buy goods for me, to the amount of $1853, and I allow him & dollars per cent. for his service, what sum must I pay him? Ans. $13.89. Compound Interest is that which arises from a principal increased by its interest, as the interest becomes due. RULE. Find the amount of the given principal for the first year, by simple interest; this amount will be the principal for the second year, and the amount of this principal found as before, will be the principal for the third year, and so on. From the last amount, subtract the given principal, and the remainder will be the compound interest, EXAMPLES.. 1. What is the compound interest of 500L. for 3 years, at 5 per cent.? Ans. 78L. 16s. 3d. 2. What is the compound interest of 450L. for 3 years, at 5 per cent. per annum? Ans. 70L. 18s. 7 d. 3. What is the compound interest of 760L. 10s. for 4 years, at 6 per cent. per annum? Ans. 199L. 12s. 2d. |