Firft, per cafe firft of intereft accounts we have. 562.962 X 7 X .05 + 362.962490l. Then per cafe fecond of prefent worths, &c. 10 X .5 .5 Then 10.5 •5 X 9 + 10X 2 X 490 X 2 = 601. Rebate or Difcount by Decimals. Cafe ft. When any fum to be discounted, time and rate per cent, are given, to find the present worth. R ULE. Divide the fum to be difcounted, by the product of the ratio and time, +1, and the quotient is the answer. What is the present worth of 3571. ros. to be paid 9 months hence, rebate at 6 per cent? First 3571. 10s.£357.5, 9m. .75 year, and the ratio .061. 357-5 357.5 7.75 X .06 +1 3421. 2s. id. anfwer. 1.045 Cafe 2d. When prefent worth, time and rate per cent are given, to find the fum to be be difcounted. ULE. Multiply the present worth by the time, R. and that produd multiplied by the ratio gives 2 number, which added to the prefent worth is the fum required. If the present worth of a fum of money due 9 months hence, allowing 6 per cent, be 3421. 2s. id. + what is the fum due ? Firft 3421. 25. 1d. £342.105263, &c. as before. 4 Then 342.105263 x.75 X .06 +342.105263= £357.5 the answer. Cafe Cafe 3d. When the fum to be discounted, prefent worth, and time are given, to find the rate per cent. RU ULE. Divide the difference of the fum to be discounted and prefent worth, by the product of the prefent worth and time, the quotient is the ratio of the rate. At what rate per cent will 3571. 10s. payable g months hence produce 3421. 25. 2d. 1. for prefent མ payment ? 3571. 10s. £. 257.5, 3421. 2s. id. I L. 342.105263. · 357.5-342.105263. 342.105263 X .75 100: 6 per cent the answer. .06 then 1.06 :: Cafe 4th. When the fum to be discounted, prefent worth and rate are given; to find the time. RULE. Divide the difference of the fum to be discounted and prefent worth, by the product of the present worth and ratio, which quotes the time. The present worth of 3571. 10s. due at a certain time to come is 3421. 2s. id. 44 at 6 per cent, at what time should the fum have been paid without any rebate ? Sol. 357-5-342.105263 75 year or 9months. Equation of Payments by Decimals. To find the true equated time, for the payment of a fum of money due at several times. RU bate. ULE ft. Find the prefent worth of each payment for its respective time, per case first of re 2d zd Add all thofe prefent worths into one fum, which fubtract from the fum to be discounted, and divide the remainder by the product of the faid fum of prefent worths and ratio of the rate, the quotient is the equated time. Admit Adam owes Noah 800l. whereof zool is due at 3 months, 200l. at 4 months 2001. at 6 months, and 200l. at 9 months, but by agreement the whole is to be paid at once, allowing rebate at 6 per cent, query the true equated time." Firft 3 months.25 year, 4m0.3. year, 6mo. .5 year, and 9mo..75 year, then as 100: 6 :: 1.06 the ratio of the rate. Extraction of the Square Root. The fquare root of a number is fuch a part of that number ás multiplied into itself, that is fquared produces the number propofed, as the fquare root of 36 8 6 because 6×6=36. RULE. Firft point the given number over units place, and alfo over every other figure, both integers and decimals. Thus, 7468247 is pointed. Alfo 17218. 4768 points. Thus. 47218.4768 &c. Secondly Secondly, put the root of the first period in the quotient, and its fquare under the period ;fubtract the fquare from the first period, and bring down the next period as in divifion. Thirdly. Double the root for a divifor, and confider how often it will go in the dividend, admiting the units place of the divifor a blank; which refult put in the root, and in the blank of units place in the divifor. Fourthly multiply the divifor by the new figure in the root, which product fubtract from the divided, and to the remainder bring down another period; and proceed to divide again as directed in the third article. What is the fquare root of 3637291 ? RU Fraction. ULE. Reduce the fraction to its lowest terms, and extract the root of both parrs for the answer, but if the fraction be a furd, reduce it to decimals and extract its root. Thus, ✓ 64 = ✓ = answer. And And 47 8 = .870637.933 + 349 To extract the Square Root of a mixed Number. ULE. Reduce the fractional part to a decimal, which join to the integcral part, and extract its root, Thus 8423 = ✓ 842.75 29.03015+ The use of the Square Root. 1. To find a mean proportioual between any two given numbers. RULE. The fquare root of the product of the two given numbers is the mean fought. Required a mean proportional between 16 and 64 ? Sol. √64 × 16 32. for 16: 32 :: 32: 64 2d. To find the fide of a fquare equal to any prop ofed fuperficies. RULE. The fquare root of the area or content of any fuperficies, is the fide of a fquare equal. A gardener being ordered to inclofe, in form of a fquare an acre of ground; begs to know the length of each fence in yards? Sol. N. B. 10 chains in length, one chain broad makes a statute acre, that is 220 yards X 22 is equal to 4840 yards, orone acre ftatute measure. Hence ✓ 4840 69.57 yards the length of each fence, which was required. 3d. The area of a circle given, to find its diameter. RULE, |