EQUATION OF PAYMENTS. Equation of Payments is a method of finding when any number of notes or bonds, due at different times, may be all paid at once, without loss to debtor or creditor. RULE.** Multiply each payment by its time; divide the sum of the products thence arising, by the sum of all the payments, and the quotient will be the equated time required. EXAMPLES. 1. A owes B a bond for $100 dollars, due two months hence, and one for $500, due 19 months hence; what would be the equated time for paying them both at once? * Much contention has arisen about the correctness of this rule. The rule presumes, that the interest of all the sums which are paid after they become due, is equal to the interest of the sums which are paid before they become due; and is susceptible of plausible demonstration, which is unnecessary to exhibit here, as any one can easily convince himself by a simple process. My own opinion is, that the equated time should be so adjusted, that the interest of all the sums paid after they 2. A man purchased a plantation for $10000, pay-able in annual payments of $1000 each; but they afterwards agreed to settle it all at once, by fixing upon a time that neither should be a loser. Required, the time? Ans. 5 years. 3. A merchant bought a quantity of goods, amounting to $10000, to pay in equal proportions, at 2, 4, 6, and 9 months, but afterwards agree to pay the whole in 5 months; which of them, debtor or creditor, had the advantage? By rule, 54 months is the equated time; but if payment be made at the end of five months, the creditor has the advantage; for his money will bring him more interest than the discount, (forbearing 54 months) will serve the debtor. 4. A owes B 5 bonds, for $945 each, payable at 3, 9, 11, 19, and 29 months; what time might they all be paid at once? Ans. 144 months. 5. Suppose a debt was discharged in the following manner; in hand, in 3 months, of in 5 months, and the residue in 11 months; might it have been sooner discharged without loss to debtor or creditor? It is a rule in law that real property cannot be condemned and sold for debt, if it will rent for as much as will pay the debt and costs, with interest, in seven To find the annual rent which any property years. should bring, in order to discharge a given debt in seven years; or, to know whether a property (according to law) should be condemned for any debt, or not, is a matter but superficially understood by most men: become due, should be precisely equal to the discount of all the sums which are paid before they become due. This opinion can be maintained by equally plausible demonstration. Here I shall drop the subject without further comment. In order to remove this difficulty, I will here insert a correct theorem, taken from page 23, Analyst.* 1. Say amount of debt, interest, and costs, now due against a property=1000, and time seven years; the lawful rate per cent being 6, amount of $1 for 1 year 1.06; our theorem will then literally 1.06—1 × 1.06 | stand, $1000 x 1.067-1 =1000 X.17913 =179.13 Ans. Now, because .17913 comes so very near to .18, we may safely reject the former and use the latter. If any debt be multiplied by 18, and two places cut off to the right hand of the product, it will give the answer near enough for practice. Take the first example, 1000 x 18-18000, two figures being cut off, leaves 180, which is only 87 cents too much, in a debt of $1000. 2. What annual rent would be sufficient to pay the amount of debt, interest and costs (upon a property) amounting in the whole to $4000, in 7 years? 4000 X.18-720 Ans. 3. A property which rented annually for $359, was condemned by a court of inquiry, for an amount of debt against it of $2300; was the condemnation lawful? 2300 X.18=414. Now, because this sum exceeds 359 by $55, the condemnation was lawful. 4. A property, worth an annual rent of $750, has against it $3000 of debt, should it be condemned? 3000 X.18=540. Now, because this is less than -750, by a considerable sum, the property should not be condemned. X * General form of the theorem is as follows, viz. x=ɑ - 1x p2 In which a=sum which may be drawn daily, weekly, monthly, quarterly, or yearly; a=sum forborne at interest; drawing, one day, one n=whole time. amount of $1 for the time of week, one month, or one year; BUYING AND SELLING STOCKS. Stocks are funds established by government, or individuals, in a corporate capacity; the value of which is fluctuating. The value of stock, at any rate per cent above or is found by the following below par, RULE. Multiply by the rate per cent, and divide by 100, or point off two decimal places to the right of the rate per cent, (it then becomes a ratio;) multiply the stock by such ratio, and the thing is done. EXAMPLES. 1. What is the amount of 3756 dollars national bank stock, at 130 per cent. 3756 x 1.30=4882.80 Ans. Second method. 2543756 5=939 187.80 $4882.80 Ans. 2. What is the value of 6000 dollars worth of bank stock, at 93 per cent? Ans. $5580. 3. What amount of stock, at 873 per cent, can be purchased for 9000 dollars? Ans. $10285.71+ 4. What is the amount of 8750 dollars of 8 per Ans. $10062.50. cent stock, at 115 per cent? 5. What is the amount of 9000 dollars of 6 per cent stock, at 87 per cent? Ans. $7875. dollars 3 per cent Ans. $5343.75. These stocks are instituted for the support of government. |