12. A regiment of soldiers, consisting of 976 men, are to be new clothed, each coat to contain 24 yds. of cloth, that is 15 yd. wide, and to be lined with shalloon, yd. wide; how many yards of shalloon will line them? Ans. 4531 yds. 1 qr. 24 na. SIMPLE INTEREST BY DECIMALS. A TABLE OF RATIOS. *་ར•ར་་་་་ས་ར་རས་་་་་་་་་་་་ RATE PER CENT. RATIO, RATE PER CENT. RATIO. RATIO is the simple interest of £1, or $I for one year at the rate per cent. agreed on. RULE Multiply the principal, Ratio and Time continually together, and the last product will be the interest required. EXAMPLES. 1. Required the interest of 537 dolls. 58 cts. for 4 years and 6 months, at 5 per cent. pr. annum, simple interest. $537.58 principal 26.8790 interest for 1 year. 1343950 1075160 $120.95550 Ans. 120 95 cts. 5 m. &c. 2. What is the interest an $268 17 cts. for 3 years and 9, months, at 4 pr. cent, simple interest? Ans. 268.17 X .045 X 3.75 45.2536875 $45 25 cts. 3 m. 3. What is the interest of 1181. 9s. for 1 year and 6 month at 6 pr. cent pr. annum? 4 Required the amount of 648 at 5 pr. cent, simple interest. Ans. 101. 13s. 2d. 2 qrs. dolls. 50 cts, for 12.75 years 5. What is the amount of 691. 8s. Ans. $1103 26 cts. + for 3 years, 14 months, at Ans. £81 6s. 6d. 3 qrs. CASE II. The AMOUNT, TIME, and RATIO given, to find the PRINCIPAL. RULE. Multiply the ratio by the time, add unity to the product for a divisor, by which divide the amount, and the quotient will be the principal. EXAMPLES. 1. What principal will amount to 264.3125, in 5 years, at 5 pr. cent pr. annum ? .05 X 51= 1.25) 264.3125 (211.45 Ans. 2. What principal will amount to $658.53550, in 4 years, at 5 pr. cent.? 3. What principal will amount to and 9 months, at 44 pr. cent? 4. What principal will amount to and 9 months, at 5 pr. cent? CASE III. Ans. $537.58 cts. $313.4236875, in 3 years Ans. $268 17 cts. 956 10s. 4.125d. in 8 years Ans. £645 15s. The AMOUNT, PRINCIPAL, and TIME given, to find the RATIO. RULE. Subtract the principal from the amount, divide the remainder by the product of the time and principal, and the quotient will be the ratio. EXAMPLES. 1. At what rate pr. cent, will 8950 75 cts. amount to $1235. 9750, in 5 years? 2. At what rate pr. cent will $715.45 cts. amount to $94.54940, in 2 years and 5 months? Ans. 6 pr. cent. Ans. 4 pr. cent. 3. What rate pr. ct. will $268.17 cts. amount to $313.4236875, in 34 years? 4. At what rate per cent will £319 5s. amount to £62.253750 in 3 years and 3 months? Ans. 6 per cent. CASE IV. The AMOUNT, PRINCIPAL, and RATE per cent given, to find the TIME. RULE Subtract the principal from the amount, divide the remainder by the product of the ratio and principal; and the quotient will be the time. FXAMPLES. 1. In what time will 8537 58 cts. amount to $658.53550, at 5 pr. cent pr. annum? From the amount $658.55550 Subtract the principal 537.58 537.58 X .05 26.8790)120.95550(4 years answer. 2. In what time will $268 17 cents amount to $313.4236875, at 4 per cent per annum? Ans. 3 years 9 months. 3. In what time will $950 75 cents amount to $1235.9750, at 6 per cent per annum? Ans. 5 years. 4. In what time will £319 5s. amount to £381.503750, at 6 per cent? Ans. 3 years. TO CALCULATE INTEREST FÓR DAYS. RULE. Multiply the principal by the given number of days, and that product by the ratio; divide the last product by 365, and the quotient will be the interest required. EXAMPLES. 1. What is the interest of 1781. 15s. for 87 days, at 6 per cent per annum? 178.75 X .87 X .06 $36.5500 365 = 2.2891 = 21. 5s. 9d. 1 qr. Ans. As the process of division is generally more tedious than that of multiplication, it is often convenient to substitute one for the other. Now if we substitute, in the place of 365, the reciprocal of that quality; that is, the quotient arising from dividing 1 by 365, we shall have a number which multiplied into the principal, will give the same result, as dividing by its corellative quantity; Thus, 1÷365= 00274, therefore to multiply a given number by 00274,* is equivalent to dividing the same number by 365. 2. What is the interest of 8 100, for 75 days, at 6 pr. cent. pr. annum ? 100 X 75 X 06 X .00274 = 123c. 3m. Ans. 3. What is the interest of S 148 50 cts. for 96 days, at 5 pr. cent pr. annum ? Ans. 95c. Sm. 4. What is the interest of & 312 for 25 days, at 71 pr. cent? Ans. 160c. 3m. 5. What will £5.5 amount to in 256 days, at 4 pr. cent pr. annum ? Ans. 5 12s Ild.† *Note. The cyphers on the left may be always neglected, by observing to point off 5 figures of the product, on the right for decimal parts. 1 1.05 ར་ར་་མ་་་་པར•ར •ར་་་ར་་ས་ ་་་་་ར་ར་་་་འ ་་་་་་་ པར་འ�བ་་བན་བ 1.06952380943396 || 1·00416 1.005 2 1.10 1.12 909091 892857 1.00833 1.010 345 1-15 1.20 51.25 1.18 869555 .847457 1:01249 1.015 •806451 1.01666 1.020 1.30 800000 769230 1.02083 1.025 1.30 I-36 7692307352941.02499 Mont 67890 1.030 1.35 1.40 1.427407 40 704225 1.02916 1.035 1.48714286 10 675675 1.03333 ¦ 1.040 67.89 10 1.04583 1.055 11 60240905000 | 1.060 | 12 1.70 1-84 588235 543478 Shewing the Rebar 1.90571448 .526315 or Present worth of Dollar, or 1 Pound, fo - 16 1.80 1.96555555510204|| Months dicounting a 2.02.540540 4950495, and 6 per Cent. Sim 480769ple Interest. 17 1.85 •467289 .454545 མ་ར་་ས་་་་་་་་ ་ར་་ར་་ར་་ར་་་བར་ 99585 99502 .357143 95617 .9478€ 11 2.86 393157 ⚫349650 95238 94339 12 2、ན་ཅནཔ་བ*4+++ར3+ར»ན་རདཱིབ་ 3+འདི CONSTUCTION OF TABLES. &c. The two first give the AMOUNT, and REBATE, or PRESENT WORTH of $1, or 1, from 1 to 31 years inclusively, at 5 and 6 pr. cent. Simple interest. They are calculated by making 1 dollar, or 1 pound the PRINCIPAL in the first, and 1 dollar or 1 pound the AMOUNT in the second; or dividing unity by the srveral numbers in the first TABLE, gives the numbers in the second TABLE. The third and fourth Tables are of the same nature with the first two, and are therefore subject to the same principle of construction. APPLICATION AND USE OF THE PRECEEDING TABLES. CASE I. To find the AMOUNT of any given sum for years and months, at 5, and 6 pr. cent, Simple Interest. RULE. To the Tabular number found in Table I, under the given rate and opposite the time in years, add the number found on the right of the decimal point in Table III, under the given rate and opposite the months, and multiply this sum by the principal; and the product will be the amount sought. EXAMPLES. 1. What will 100 amount to in 7 years and 8 months, at 6 pr. cent pr. annum, Simple Interest ? Tabular number 1.42 = amount of $1 for 7 years. 2. Required the amount of $318 50 cents, for 5 years, at 6 per cent per annum. Ans. 414 05cts. 3. What will $753 25 cents amount to in 4 years and 7 months, at 5 per cent per annum ? Ans. $925 86c. 377m. 4. Required the amount of 1121. 10s. for 3 years and 5 months, at 6 per cent. Ans. 1351. 11s. 4d. 5. Required the amount of 1801. 8s. for 11 months, at 6 per cent per annum. Ans. 1901. 6s. 5d. 1 qr. CASE II. To find the Interest of any given sum for years and months, at 5 and 6 per cent. RULE. 1. Find the amonnt as before, from which subtract the princi pal, and the remainder will be the interest. |