andwishes to pay the whole at once; I demand the equated Ans. 13 months. time. 1. What is Discount? Questions. 2. What is the present worth of any sum ? 3. (Rules.) How do you find the Discount of any sum? 4. How do you find the present worth? 5. When several sums are payable at different times, how do you find the present worth? 1. What is Equation of Payments ? 2. What is the rule for Equation of Payments? ANNUITIES AT SIMPLE INTEREST. An annuity is a sum of money payable every year, or for a certain number of years, or forever. When the annuity is not paid at the time it becomes due, it is said to be in arrears. The sum of all the annuities, together with the interest due on each for the time they have been forborne, is called the amount. 1. To find the amount of an Annuity. RULE. 1. Cast the interest on the given annuity for one year, then for two years, three years, four years, &c., up to the given time, less 1. Then multiply the annuity by the given number of years, and add the product to the whole interest, and the sum will be the amount required. EXAMPLES. 1. If an annuity of 200 dollars per annum remain unpaid, (that is, in arrears,) 6 years, what is the amount due, reckoning interest at 6 per cent.? The interest of $200 for 1 year is $12,00 24,00 36,00 48,00 60,00 1200,00 Ans. $1380,00 2. If a salary of $325 per year remain unpaid, or in arrears, for the term of 5 years, what amount is then due, interest at 6 per cent? Ans. $1820. 3. If a man, having an annual pension of $75 a year, receive no part of it until the end of 7 years, what is the amount due, interest at 5 per cent ? Ans. $603,75. 2. When an annuity is bought off, or paid all at once, at the beginning of the first year, the sum that is paid for it is called the present worth. To find the present worth of an annuity at Simple Interest. RULE. Find the present worth of each year by itself, discounting from the time it falls due, and the sum of all the present worths will be the present worth,required. EXAMPLES. 1. What is the present worth of an annuity of $500, to continue 4 years, at 6 per cent per annum ? As 106 100: $500: $471,6981+pres. worth 1st year. 112 100 :: 500 446,4285+ 2d year. 3d year. 4th year. Ans. $1745,0812=$1745, 8cts. 12m. 2. What sum of ready money is equal to an annuity of 100 dollars to continue 3 years, discounting at 6 per cent? Ans. $268,371. 3. What is 600 dollars yearly rent, to continue 4 years, worth in ready money at 6 per cent? Ans. $2094, 09c, 4. What is the present worth of an annual salary of 800 dollars, to continue 5 years, at 6 per cent? Ans. $3407 51,2c. 1. What is an annuity? Questions. 2. When is an annuity said to be in arrears? 3. What is the sum of all the annuities, together with their interest, called? 4. How do you find the amount of an annuity? 5. What is the present worth of an annuity? 6. How do you find the present worth of an annuity? tare, which subtract from the gross the remainder will be the net. EXAMPLES. Note. The examples in this Case are predicated on the modern custom of counting 100lbs. to the cwt. 1. In 10 casks of rice, each 4cwt. 2qrs. 15lbs., tare per cwt. 10lbs., what is the net? 2. What is the net weight of 9 barrels of potash, each weighing gross 2cwt. 3qrs. 18lbs., tare 124lbs. per cwt.? Ans. 23cwt. Oqr. 7lb. 6oz. 3. Bought 43cwt. 2qrs. 20lbs. of sugar, tare per cwt. 10 pounds; required the net weight, and its value at 8dols. 33cts. per cwt. Net 39cwt. 1qr. 8lbs. Value $327, 61c. 8m. Ans. {Value 4. What is the net weight, and value, of 24 barrels of figs, each 1cwt. 3qrs. 22lbs., tare per cwt. 124lbs., at 7 cents Net 41cwt. 1qr. 12lbs. {Value $289, 99cts. 5. In 83cwt. 3qrs. 15lbs. gross, tare per cwt. 15lbs., what is the net weight? Questions. Are there any such allowances now made as "Tret and Cloff? 1. What is Gross weight? 2. What is Tare? 3. What is Net? I. If the question be an Invoice, how Ans. 71cwt. 1qr. 64lbs. do you find the net weight? II. When the tare is so much per box. cask, bag, &c., how do you find the net weight? III. When the tare is at so much per ewt., how do you find the net weight? BARTER Is the exchanging of one commodity for another; and directs merchants and traders how to make an exchange without loss to either party. RULE. Find the value of the article whose quantity is given; then find what quantity of the other article, at the proposed rate can be bought for the same money. EXAMPLES. 1. What quantity of sugar, at 11cts. per pound, must be given for 11lbs. of indigo, at $2,50 per pound? First see what 11lbs. of indigo will come to at $2,50 per pound. Thus, $2,50 × 11=$27,50. Then $27,50cts. 11cts. 250lbs. Answer. 2. How much tea, at $,38 per lb., must be given for 24bush. of wheat, at $1,25 per bushel? Ans. 781 lbs. 3. How much salt, at $1,50 per bushel, must be given for 15bush. of oats, at $,37 per bushel? Ans. 3bu. 3pks. 4. A man sold 356lbs. of pork, at 8 cents per pound, for which he received 10 dollars in money, and the rest in corn at $,75 per bushel; how much corn did he receive? Ans. 241 bushels. [Find what 356lbs. of pork will come to, then deduct the $10 from that sum; then find how many bushels may be had for the remainder.] 58 5. How much rice, at $4,68 per cwt., must be given for 3 hundred weight of raisins, at 8cts. per pound? Ans. 6cwt. 2 quarters 22 pounds. 6. A and B barfered, A had 250lbs. of sugar, at 11cts. per pound, for which B gave him 11lbs. of indigo; what was the indigo rated at per pound? Ans. $2,50. 7. A delivered B 3 hogsheads of brandy at $1,08 per gallon, for 135 yards of cloth; what was the cloth per yard? Ans. $1, 51cts. 2 mills. 8. A farmer delivered to a merchant 5 cords of wood, at $6,50 per cord; in pay he received 16 gallons of molasses at $,37 per gallon, 2 barrels of flour at $6,25 per barrel, 2yds. of broadcloth at $4,37 per yd., and the rest in money; how much money did he receive? Ans. $51. The ready money and barter price of one article, and the ready money price of the other given, to find its barter price. 9. A has linen cloth worth $,42 per yard, ready money, but in bartering he will have $,50 per yard; B has broad cloth worth $4,50 per yard, ready money; at what price ought B to rate his broadcloth per yard to be in proportion to A's bartering price? As 42: 50 :: 450: 535-$5, 35 cts. Therefore, B must rate his broadcloth at $5,35% per yard, to be in proportion to A's bartering price. 10. A has 240 bushels of rye, at $0,90 per bushel, which he barters with B at $0,95 per bushel, for wheat worth $1,12 per bushel, ready money; what ought B to rate his wheat at per bushel to be in proportion to A's bartering price, and how many bushels of wheat must A receive for his 240 bushels of rye ? Ans. S Bartering price of B's wheat $1,18%. LOSS AND GAIN Is a rule by which merchants and traders discover their profit or loss in trading. It also instructs them how to rise or fall in the price of their goods, so as to gain or lose so much per cent, &c. EXAMPLES. 1. Bought 35 yards of broadcloth for $131, 25cts., and sold it again at $4, 25cts. per yard; what did I gain on the whole? Ans. $17,50. 2. Bought a hogshead of sugar, containing 83cwt. for $67,60, and sold it out at 103cts, per pound; what did I gain on the whole ? Ans, $35,30. 3. Bought 125 yards of cambric for $62, 50cts., and sold it again at $0, 45cts. per yard; how much did I gain or lose on the whole? and how much on each yard? Lost on the whole $6,25, Ans. On each yard $0,05. 4. Bought a chest of tea, weighing 75lbs., at 31 cts. per lb. and sold it again at 42cts. per pound; did I gain or lose, and how much? Ans. Gained $7,87. 5. Bought a hogshead of rum containing 120 gallons, at 56cts. per gallon: paid for duties $6,00, and for carting $2,00, and by accident 10 gallons leaked out; at what rate |