PROBLEM XVI. Given the ratio, the last term, and the sum of the series, to find the number of terms. RULE. 1. Multiply the difference between the sum and the last term by the ratio, and note the product. 2. Subtract this product from the sum, and note the remainder. 3. From the logarithm of the last term subtract the logarithm of the remainder. 4. Divide this last remainder by the logarithm of the ratio, and the quotient, plus unity, will give the number of terms. EXAMPLE. If the ratio be 3, the last term 54, and the sum of the series 80; what is the number of terms? From the sum=80 Take the last term=54 Remainder 26 Multiply by the ratio= 3 Product=78 From the sum=SO Take the product=78 Remainder-2 From the logarithm of 54-1.73239 Take the logarithm of the remainder = .30103 Divide by the logarithm of the ratio=47712)1-43136(3+1=4 Ans. PROBLEM XVII. and XVIII. Given the number of terms, the last term, and the sum of the series, to find the first term and the ratio. The solution of these two Problems being very tedious by the Theorems, they may be solved by a very short operation; thus, Divide the sum of the series by the difference between the sum and the last term; the quotient will give the ratio, and the remainder, after the operation, the first term. EXAMPLE. If the number of terms be 4, the last term 54, and the sum of the series 80; required the first term and the ratio? From the sum=80 Take the last term=54 Divide by the difference=26)80(3 the ratio. 78 The first term= 2 The INTEREST is a Premium allowed by the Borrower to the Lender, according to a certain Rate per cent. agreed on; which by law is stated at 6 per cent. per annum. Principal is the money lent. Rate is the sum per cent. agreed on. Amount is the Sum of Principal and Interest. Simple Interest is that which is allowed on the Principal only. Note. By this Rule, Commission, Brokerage, Insurance, pur. chasing 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 fig. ures 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 a of year; and for days, the aliquot parts of 30. 1. What is the interest of 5731. 13s. 94d. at 6 per cent. per annum ? £.573 13 9 Answer, .34 Ss. 5d. 2. What is the interest of 3291. 17s. 61d, for 3 years, 7 months, and 12 days, at 5 per cent. per annum. £.329 17 64d. 16.49 7 8 20 5 6 mons. Then, Ans. £.59 13s. 16 9 10 interest of 1 year 49 9 7 do. of 3 years f 3. What is the interest of 347 dollars 50 cents, at 6 per cent. per annum for a year? D.347.50 6 20-8500 Ans. D.20 85c. 4. What is the interest of D.797 13c. at 6 per cent. per annum, for 8 months? D.797.13 31-8852 Ans. D.31 88c. 5m. 5. What is the interest of D.649 17c. at 6 per cent. per annum, for 15 months? D.649.17 48-68775 Ans. D.48 68c. 74m. 6. Required the amount of £.725 12s. 6d. at 5 per cent. per ann. for a year? 5725 12 6 36 57/1/20 7. What is the amount of D.560 50c. at 6 per cent. for 16 months? 8. What is the interest of D.150 75c. for 1 month, at 6 per cent. per annum? 150-75 75375 Ans. 75cts. 34 mills. So that any number of dollars, considered as so many cents, is the interest for 2 months, at 6 per cent. COMMISSION, OR FACTORAGE, Is an allowance of so much per cent. to a Factor or Correspondent, for bying and selling goods. 9. Required the commission on £.436 9s. 6d. at 3 per cent. 2...F L.436 |