DISCOUNT. 84 the interest by multiplying the principal in dollars, by the number of days, dividing by 6 for the answer in mills. This method gives too much; and by computing the interest on the whole note to be discounted, produces a second excess, which they deduct, and advance the balance to the holder, thus charging interest on the part deducted, as well as the part advanced : such errors in large sums are considerable, 2. What is the present worth and discount of $75 for 2 years, at six per cent. per annum ? Ans. $66.96,5; and $8.03,5 discount. 3. What is the present worth of £100, one half payable at 4 months, and the other half at 8 months; discount at 5 per cent. per annum ? Ans. £97. lls. 4. + 4. What is the difference between the interest on $600, at six per cent. per annum, for six years, and the discount on the same sum, at the same rate and for the same time? Ans. $57.17,6+ 5. What is the present worth of $350, payable in six months, at a discount of six per cent. per annum? Ans. $339.80,5+ 6. Bought a quantity of goods for $250 ready money, and sold them for $300, payable 9 months hence--what was the gain for ready money, supposing a discount to be made of six per cent. ? Ans. $37.08+ 7. Suppose a debt of $810 were to be paid three months hence, allowing five per cent. discount—what is it worth in cash ? Ans. $800. 8. A has B's note of hand for $10000, payable 93 days hence, allowing a discount of six per cent. per annum-required its equivalent value in ready money, and discount; and what its present value and discount at bank; likewise its equivalent interest for the same time and rate per cent. per annum? Ans. $9849.5268+ its equitable value in ready money, $150.4732. discount And $152.77,2, its equitable interest. 9. A is indebted to B in $1012, whereof $432 is to be paid in 12 months, and $580 in 2 years; but if A pays this debt immediately, allowing a discount of 8 per cent. per annum, how much must he pay? Ans. $900 in ready money. COMPOUND INTEREST BY DECIMALS. COMPOUND INTEREST is that which arises from any princi. pal and its interest put together, as the interest becomes due; and for that reason is called Compound Interest. When the principal, rate of interest, and time are given, to find either the amount or interest. RULE. 1. Find the amount of one dollar for one year, at the given rate per cent. 2. Involve the amount thus found to such power as is denoted by the number of years. 3. Multiply this power by the principal or given sum, and the product will be the amount required, from which subtracting the principal the remainder will be the interest. EXAMPLES. 1. What is the compound interest of 600 dollars for 4 years, at six per cent. per annum ?' (First find the ratio by dividing the rate per cent. by 100: thus too=.06, ratio, or interest on one dollar for a year.) $1 and interest 1 year=1.06 amount Multiply by 1.06 636 106 1.1236=2d power Multiply by 1.1236 1.26247696=4th power Multiply by 600 $757.48c.6m.17600 =amount Subtract 600. $157.48cts.6 mills, interest required. 2. What is the amount of 1500 dollars for 12 years, at 3.5 per cent. per annum? Ans. $2266.6029. 3. What is the compound interest of 100 dollars for 2 years, at six per cent. per annum? Ans. $12.36. 4. What sum will 450 dollars amount to in 3 years, at five per cent. per annum? Ans. $520.93,125. CUBICAL MEASURE. To find the solid or cubic measure of wood and bark, store, grain, coal, &c. RULE. Take the measurement in feet and tenths, and multiply the length and width together, and their product by the height .or depth, the (last) product will be the number of solid feet, and decimal parts of a foot, which divide by 128 for cords, or 24.75 for perches, or 1.24446 for bushels of struck measure, or 1.47779 for bushels of heaped or rounding measure. Or, take the measure in inches, which cube as before, and divide by the cubical inches contained in a cord, perch, bushel, &c. See the denominations of Cubic or solid measure. NOTE.--In some sections of the country, stone is bought and sold at 16.5c.ft.=28512c.in. per perch. Where this measure is the cus tom of the country, divide the cubic measure in feet by 16.5, or the eubic inches by 28512 for the measure in perches. EXAMPLES. 1. Required the quantity of feet, and the value, of a load of bark, 16 feet in length, 31 or 3.50 feet in width, and 3% or 3.75 feet in height, at $6 per cord ? Ans. 210c.ft. the value $9.84,375. in. Thus 3.5 Or, 6=1 16 16 3 6 56.0 3.75 48 2250 1875 6=156 3 9 Ans. 210.00c.ft. 168 3= 28 As 210 : 128 :: 6 : 9.84,375 Ans. 14 Ans. 210c.ft. 2 In a pile of stone 20 feet in length, 8.5 feet in width, and 4.25 feet in height, how many perches ? Ans. 29.191 +ph. 3. Required the quantity of grain in a bin 12.25 feet in length, 6.5 feet in width, and 4.75 feet in depth or height. Ans. 303bu. 3p. 5+qt. $12 per 4. Required the quantity of charcoal in a box (or wagon,) 15.5 feet in length, 3.5 feet in width, and 3 feet in height. Ans. 110bu. 4qt. + 5. Required the number of cubical feet in a stick of scantling 30 feet in length, 1} feet in width, and } foot in depth. Ans. 221 feet. 6. Suppose a deck-load of bark to measure 30 feet in length, 22.5 feet in width, and 8.4 feet in height-required the number of solid feet, number of cords, and value, at cord. Ans. 5670ft.=44&cd. and 6ft.-value, $531.5625. 7. How many perches of stone are there in a wall 48.25 feet in length, 1.5 feet in width, and 12 feet in height? Ans. 35.09+ perches. 8. Required the quantity of wood in a tier 644 feet in length, 4 feet in width, and 4 feet in height. Ans. 8.0625=816 cords. 9. In a pile of stone 25 feet in length, 12.5 feet in width, and 5.5 feet in height, required the cubical feet, the number of perches, and the value at 75cts. per perch. Ans. 1718.75c.ft.=69.444ph-value, $52.08,3+ 10. How many bushels of corn are there in a granary measuring 147 inches in length, 78 inches in width, and 57 inches in depth or height? Ans. 303bu. 3p. 5qt. 1pt. Note. -For other examples, see page 145. Oth SQUARE MEASURE. RULE. Multiply the l ngth in feet by the width in inches, and tise product by the depón or thickness in inches; divide the last product by 12 for the admeasurement in feet. Or, mul tiply the length in feet by the width in inches, and that product by the depth or thickness in feet, if any, and take parts the inches, if any, for the measurement in feet. EXAMPLES. 1. Required the number of feet in a board 20 feet in length, 9 inches in width, and 14 inches in thickness. Ans. 22.5 feet. 22.5ft. Ans. 2. In a stick of scantling 16 feet long, 3 inches wide, and 5 inches in depth, how many feet? Ans. 20 feet. 3. In a stick of timber 22.5 feet in length, 6 inches by 3.5 inches, how many feet? Ans. 39.375ft.=39ft. 54in. 4. Required the admeasurement of a board, 30 feet in length, and 2 feet 4 inches in width. Ans. 70 feet. 5. To floor a room 20 feet square, how many feet of board 1 inch thick will it require ; how many feet of 14 inch board, and how many of 14, allowing } for waste? Ans. 400ft.; 500ft. ; 625ft. NOTE.-To ascertain the waste---if } is allowed, add to the wrought stuff required; if 5 waste, add }; if waste, add 3, and so on: thus, if it takes 500 feet of wrought boards to cover a floor, how much unwrought stuff was there, allowing for waste? Ans. 600ft.-thus, wrought stuff, 500-:-5=100+500=600, unwrought stuff. 6. Suppose a stick of scantling to be 14 feet in length, 1 foot 4 inches in width, and 2 feet 3 inches in depth, how Ans. 504 feet. The number of feet, width, and depth being given, to find the length. many feet? RULE. Multiply the number of feet the board or scantling con. tains by 12, and divide this product by the product of the width and depth in inches; the quotient will be the length in feet. EXAMPLES. 1. Required the length of a board that contains 16 feet, and is 4 inches in width, and 1 inch in depth. Ans. 48 feet in length. 2. Required the length of a stick of scantling containing 504 feet, that is 27 inches in depth, and 16 inches in width. Ans. 14 feet in length. |