EXAMPLES IN GEOMETRICAL PROGRESSION, To be solved by those formulæ in the Table, of which the rules are not given in the Problems. 1. The least term is 2, the greatest term 4374, and the sum of the series 6560; required the number of terms. This is solved by the 2nd rule of Case 4 in the table. Ans. 8. 2. If the ratio be 4, the last term 3072, and the sum of the se. ries 4095; what is the first term and the number of terms? Ans. The first term 3, the number of terms 5. Wrought by Case 9. 3. Given the number of terms 4, the last term 54, and the sum of the series 80, to find the first term and ratio. Ans. The first term 2, the ratio 3. Wrought by Case 9 in the table. INTEREST. INTEREST is a premium allowed by the Borrower to the Lender, for the use of his money. It is estimated at a certain number of pounds, dollars, &c. for each hundred pounds, dollars, &c. for a year; and in the same proportion, for a less or greater um, or for a longer or shorter time. Hence, interest is said to be so much per cent. or per centum, per annum. The Principal is the sum lent. The Rate is the premium per cent. agreed on.* SIMPLE INTEREST. Simple Interest is that which is allowed on the Principal only. Note. By this Rule, Commission, Brokerage, Insui ince, purchasing Stocks, or any thing else, rated at so much per cent. are calculated. GENERAL RULE. 1. Multiply the Principal by the Rate, and divide by 100 (or cut off the two right hand figures in the Pounds) and the quotient, or left hand figures will be the answer in Pounds, &c. the right hand figures being reduced and cut off as at first. If the principal be dollars, the right hand figures will be cents.† 2. For more years than one, multiply the Interest of one year by the number of years. 3. For any number of months take the aliquot parts of a year; and for days, the aliquot parts of 30. 1. What is the interest of £573 13s. 91d. at 6 per cent. per annum ? Ans. £34 8s. 5d. *Lawful or legal interest is that which is permitted by the laws of the State. It is different under different governments. In England the Rate is five per cent. In the New England States, it is six, and, in the State of New York it is seven per cent. The courts of the United States allow interest according to the practice of the State where the suit was commenced. The rules of the Courts in the States of Massachusetts, Connecticut, and New York, for computing legal interest, will be given immediately before Discount. + This rule is a contraction of a process in the Rule of Three. Thus in the 1st Example. As, 100 :: 6 :: £573 13s. 94d.: the interest for a year. And 6X £573 13s. 9jd. £34 8s. 5d. the interest. The remainder of the rule is obvious. 100 The reason of the rule in the Note above is, that as 9 is of 12 months, if the rate be 9 per cent, multiply the principal by of the months; if the rate be 8 per cent. by 3 of the number of months; and if 6, by half the months, &c. ⚫52 2. What is the interest of £329 176. 6d. for 3 years, 7 months, and 12 days, at 5 per cent. per annum. Ans. £59 138. £329 17 61d. 16.49 781/ Then, 20 49 9 17 53 do. of 1 month 9 12 do. of 10 days 1 93 do. of 2 days 3. What is the interest of 347 dollars 50 cents, at 6 per cent. per annum for a year. $347.50 Or $100 6: 347.50c.: $20.85c. 6 20-8500 Ans. $20 85c. 4. What is the interest of $797 13c. at 6 per cent. per annum, for 8 months? $797-13 31-8852 Ans. $31 88c. 5m. > What is the interest of $649 17c. at 6 per cent. per annum, for 15 months? Ans. $48 68c. 72m. 6. Required the amount of £725 12s. 6d, at 5 per cent. per annum, for a year? 5725 126 36 57 Ans. £761 18 1 7. What is the amount of $560 50c. at 6 per cent. for 16 months? $560 50 8 44.84 560.50 Ans. $605-34c. 8. What is the interest of $150 75c. for 1 month, at 6 per cent. per annum? 150-75 75375 Ans. 75cts. 3 mills. So that any number of dollars, considered as so many cents, is the interest for 2 months, at 6 per cent. and the half of it is the monthly interest. COMMISSION, OR FACTORAGE, Is an allowance of so much per cent. to a Factor or Corrèspondent, for buying and selling goods. 9. Required the commission on £436 9s. 6d. at 33 per cent. |