For 6 per cent. .06 will be a common multiplier. For 5 per cent., .05; for 5, .055, &c. They are all found by the rule of proportion as before.* LESSON 18. years at 3 per cent. per an What is the interest of 354 num? Ans. 44 dol. 31 cents. cents for 1 year, at 7 per Principal, cent.? Ans. 24.78 cents. Principal, 354 cents. Com. mul. •07 80.250 cents. 31650 cents. Com. multiplier, .035 158250 94950 one year's int. 1107.750 Ans. 4431.000 cents. My agent has bought cattle to the amount of 3452 dollars and 874 cents; how much will his commission be In the last lesson we point at the rate of two and a half off three decimals in the pro- per cent ? duct, because there are 3 in Answer, 36 dol. 32 cents. 345287.5 cents. the factors, that is, one in the Principal, multiplicand, and two in the Com. multiplier, .025 multiplier. What is the interest of £32 1s. 6d. for 5 years at 61 per cent. per annum? Ans. £ 10 8s. 5d. 3q. 4 tenths. A common multiplier is found in this case by the same proportion as that above Lesson 18, viz. If 100 pounds in a year will give 6.5 pounds interest, what will one pound give in the same time? Ans. .065 of a pound. ❤ This common multiplier can be on a memorandum, or retained in memory. PROBLEMS OF INTEREST. To find the principal when the rate per cent., the time, and the amount are given, say, "As the amount of £ 100 at the rate and time given, is to £ 100; So is the amount given, to the principal required." LESSON 23. What principal being put to interest for 5 years, at 6 per cent. per annum, will amount to 390 dollars? Answer, 300 dollars. If 100 dollars will give 6 dollars interest in one year, then in 5 years the interest will be 30 dollars; add this sum of 30 dollars to the principal 100, and the amount will be 130. Now say: If 130 amount, arise from 100 principal, what will 390 amount, arise from? To find the rate per cent., when the principal, the time, and the amount are given, say: "As the principal, is to the interest for the whole time; So is £100, to its interest for the same time." "Divide the interest last found by the time, and the quotient will be the rate per cent." LESSON 24. At what rate of interest per cent. will 300 dollars amount to 390 in 5 years? Ans. 6 per cent. Subtract the principal from the amount, the remainder will be the interest of 300 dollars for the whole time. Then say: If 300 principal in the whole time, give 90 interest, what will 100 give in the same time? 300 90: 100 Time 5 yrs. 3)90100 5)30(6 quotient or rate per cent. To find the time when the principal, the rate per cent. and the amount are given, say, "As the interest of the principal for 1 year at the given rate, is to one year; So is the whole interest, to the time required." LESSON 25. In what time will 300 dollars amount to 390, at 6 per cent. per annum? Answer, 5 years. One hundred dollars give 6 dollars interest in a year; then 300 dollars will give 18 for interest. If 18 dollars require one year, what will 90 dollars the whole interest require? Rebate, is an allowance for present payment before a sum of money becomes due. Present worth, is the sum to be paid immediately for another sum due at a future time. For instance, the sum of 200 dollars, at 7 per cent., will be due 12 months hence; what is the present worth? We can perceive that $200 will gain 14 at 7 per cent. interest, and can be taken from the debt; but this is too great a deduction: What sum at 7 per cent. interest will amount to 200 dollars in 12 months? Such a sum is the present worth required. RULE. As the amount of 100 dollars, at the rate and time given, is to 100 dollars; So is the whole debt, to the present worth required. LESSON 1. What is the present worth of 200 dollars for one year!! at 7 per cent. rebate? 100 dollars + 7 dollars interest for 1 yr. 107 amount for 1 year. Answer, 186 dol. 91 cents. ||200 dollars the whole debt. A. P. A. As the sum of 107: 100: 200 to its principal. Read thus, As the sum of 107 dollars amount, is to 100 dollars principal; so is the sum of 200 dollars amount to its principal, or to the present worth. dol. tract the present worth from 100 2d. term. the whole debt, the remain200 3d. term.der will be the rebate; viz. 13 dol. .09 cents. [worth. 1st. term, 107)20000(186.91 107 [present .930 856 .740 642 .980* 963 . 170* Remainder. 63 to be added in the proof. Thus we find that the sum 186 dol. 91 cents is the pre RULE FOR PROOF. Find the amount of the present worth for the time and at the rate per cent. given. EXAMPLE. What is the amount of 18691 cents for 1 year, at 7 per cent. interest? 18691 principal and 63 rem. 7 rate per cent. 130900 interest for 1 year. 18691 principal. 20000 cts. amount; or $200 LESSON 2. What is the present worth sent worth required. Sub- of 450 dollars payable 9 |