EXAMPLE. Find the present value of an annuity of £36 to last 6 years at 4 per cent. Ill. TO FIND THE VALUE OF A PERPETUAL ANNUITY. Rule. Find the ratio of the annuity to the interest on £1 for one year; this will be the number of pounds in the value. EXAMPLE. Find the present value of £3 perpetual annuity, interest being at the rate of 21 per cent. IV. TO FIND THE PRESENT VALUE OF A DEFERRED ANNUITY. Rule. Find the value of the annuity, supposed perpetual, and multiply this by the difference between the present values of £1, due at the time at which the annuity is to commence, and due at the time at which it is to cease. EXAMPLE. Find the present value of an annuity of £130 to commence 8 years hence, and to continue 15 years, at 4 per cent. Present value of perp. ann. of £130 = £130÷.045 = £2888.8. Present value of £1 due 8 years hence 23. .......... =.7031851 =.3633501 V. TO DETERMINE WHAT ANNUITY MAY BE PURCHASED WITH A GIVEN SUM, TO LAST A GIVEN TIME. Rule. Find the present value of an annuity of £1 for the given time; the ratio of the given sum to this will be the number of pounds in the annuity. EXAMPLE. If a person lay out £3000 in the purchase of an annuity, to continue 25 years, find his yearly income at 5 per cent. compound interest. Present value of an annuity of £1 for 25 years = 14.0939446. Def. 1. Exchange is the rule by which the money of one country is changed to that of another. Def. 2. The par of exchange is the intrinsic value of the coin of one country expressed in terms of the coin of another. Def. 3. The course of exchange at any time is the sum, which at that time, is given in one coinage for a sum in another. Def. 4. By arbitration of exchange is meant the determining the course of exchange between two places, from the known rates between each of the two and other places. Arbitration is called Simple or Compound, according as three only or more than three places are mentioned. Rules. Questions in Exchange may be worked by Practice or Proportion; questions in Simple Arbitration by Proportion, and in Compound by the Rule called The Chain Rule, Beginning with one of the places between which the course of exchange is required, write down a series of equations expressing the courses of exchange between the several places which are mentioned, always putting on the left hand the same denomination of coin, as appeared in the preceding equation on the right. Multiply together all the numbers on the right hand side, and all but the first on the left hand side; divide the first product by the second; the result will be the amount of coinage of the last mentioned place equal to the given amount of that first mentioned. EXAMPLES. 1. Exchange £735 for francs at 24.25 fr. for £1. 24.25 francs = £1 735 12125 7275 16975 17823.75 francs = £735 Ans. 2. Exchange £520: 15:0 for Prussian dollars at 6 dollars 25 groschen Ans. 35581 Pr. dol. 3558 Pr. dol. 13 groschen. 3. Exchange 3864 florins at Amsterdam with Naples at 80 florins for ducats. 4. Bills on Paris, bought in London at 25 francs 40 cents, are sold in Hamburg at 187 francs per 100 marks: what is the exchange between London and Hamburg? 5. A bill upon Hamburg is bought at 13 marks 10 sch. per £1 sterling, and sold in Amsterdam at 353 florins per 40 Banco marks; if the proceeds are there laid out in bills upon Genoa at 47 florins per 100 lire, and these again sold in Paris at 1 per cent. discount, what is the rate of exchange between London and Paris. .. £1 × 40 × 473 × 100 = 13— × 351 × 100 × 99 francs Def. Barter is the Rule by which is determined what quantity of one article is equivalent in value to a given quantity of another; or what must be the quality of an article that a given quantity of it may be equivalent in value to a given quantity of another. I. TO FIND THE QUANTITY OF ONE ARTICLE EQUIVALENT IN VALUE TO A GIVEN QUANTITY OF ANOTHER ARTICLE. Rule. Find the value of the goods received, and thence determine the quantity of goods exchanged, which may be had for the same money. Or work by the Chain Rule as in Exchanges. EXAMPLES. 1. How many yards of silk velvet at 15s. a yard may be exchanged for 125 yards of satin at 10s. 6d. a yard? Value of satin = 10s. 7d. X 125 = £65: 12:6 = £65§ 2. Bought 2 cwt. 3 qrs. 16lbs. of sugar at £3: 5:0 per cwt. and paid half in cash, and the rest in cloth at 14s. 6d. per yard; how much money did I pay, and how many yards of cloth ? The same example worked by the Chain Rule. Quantity of cloth required = 1 cwt. 1 qr. 22 lbs. sugar = 162lbs. sugar. |