between them that P shall make present pay of his whole debt, and that Q shall pay his so much the sooner, as to balance that fayour; I demand the time at which Q must pay the $250 reckoning simple interest. 50X4=200 100x8=800 50+100=15|0)100|0(62 months, P's equated time. D. mo. D. mo. 90 10 mo. mo. to. As 150 6: 250 4. Then, 10-4-6 time of Q's payment. 2. A merchant has 1201. due to him, to be paid at 7 months; but the debtor agrees to pay ready money, and at 4 months; I demand the time he must have to pay in the rest, at simple interest, so that neither party may have the advantage of the other? Debt £120 160 must be paid down. 140 must be paid at 4 months. Now, as he pays 601. 7 months, and 401. 3 months before they are respectively due, say, as the interest of 201. for 1 month, is to 1 month, so is the sum of the interest of 601. for 7 months, and of 401. for 3 months, to a fourth number, which, added to the 7 months, will give the time for which the 201. ought to be retained. Ans. 2 years and 10 months. 3. A merchant has $1200 due to him, to be paid at 2 months, at 3 months, and the rest at 6 months; but the debtor agrees to paydown: How long may the debtor detain the other half, so that neither party may sustain loss? Now as was paid 4 months before it was due, it is reasonable that he should detain the other, 4 months after it became due, which added, gives 83 months, the true time for the second payEquated time 4 months. ment. EQUATION OF PAYMENTS BY DECIMALS. RULE.* 1. To the sum of both payments add the continual product of the first payment, the ratio, and the time between the payments, and call this the first number. *Suppose a sum of money be due immediately, and another at the expiration of a certain given time forward, and it is proposed to find a time, so that neither party shall sustain loss. Now, it is plain that the equated time must fall between the two payments; and that what is gotten by keeping the first debt after it is due, should be equal to what it lost by paying the second debt before it is due; but the gain drising 2. Multiply twice the first payment by the ratio, and call this the second number. 3. Divide the first number by the second, and call the quotient the third number. 4. Call the square of the third number the fourth number. 5. Divide the product of the second payment and time between the payments by the product of the first payment and the ratio, and call the quotient the fifth number. 6. From the fourth number take the fifth, and call the square root of the difference the sixth number. 7. Then the difference of the third and sixth numbers is the equated time, after the first payment. EXAMPLES. There are $100 payable in 2 years, and $106 at 6 years hence; what is the equated time, allowing simple interest, at 6 per cent. per annum? 1st payment 100 Ratio=06 6.00 1st payment 100 200 Time between the payments=4ys. Mult. by the ratio=06 Div. by the 2d num. 12)230=1st number. 19.166+3d number. 3d number squared=367·335556=4th number. prod. of the 2d payment and 1st payment mult. by the ratio=6)424={time between the payments. 70 666+5th number. From the 4th number=367-335556 296 668890(17-224sqr.root=6th upm. Carried up. from the keeping of a sum of money after it is due, is evidently equal to the interest of the debt for that time: And the loss, which is sustained by the paying of a sum of money before it is due, is evidently equal to the discount of the delt for that time: Therefore it is obvious that the debtor must retain the sum immediately due, or the first payment, till its interest shall be equal to the discount of the second sum for the time it is paid before due; because in that case the gain and loss will be equal, and consequently neither party can be a loser. From the 3d number=19.166 Take the 6th number=17.224 Brought up. 1.942 equated time from the first payment; therefore 3 942 years =3y. 11m. 9d. whole equated time. Or, 100+106+100×·06×4 100×2×·06 100×2×·06 100x-06 2. There are $100 payable one year hence, and $106 to be paid gix years hence; what is the equated time, computing interest at 6 per cent.? Ans. 3. A debt of $1000 is to be paid, one half in three years and the other half in 6 years; what is the equated time for paying both, computing interest at 7 per cent ? Ans. EXCHANGE. THE object of Exchange is to ascertain what sum of money ought to be paid in one country for a sum of different denomina tions or of different relative value received in another, according to the course of exchange. The par of exchange respects the intrinsic value of the money of different countries compared with each other. Thus a pound sterling is equal to 4 dolls. and 44 cents in the United States; the mark banco of Hamburgh, to 331 cents; 40 marks banco to £3 sterling. If the exchange be made at the intrinsic value of the money of different countries, it is said to be at par; but if the money of one country be estimated at less or more than its intrinsic value, the exchange is said to be above par, or below par.* Owing to changes in the course of trade, to demand for money, to variations in the relative value of gold and silver, &c. the relative value of the money of two countries is liable to frequent changes. Hence the course of exchange, or the current price of exchange, must vary with these circumstances, and be sometimes above, and sometimes below, par. Tables of the course of exchange are published daily in the great commercial cities. * The Rules under Reduction of Coins are founded on the par of exchange. For the reduction of the Money, and Measures of most commercial countries to Federal and Sterling Money, and American Measures, see also the Tables of Money, Length, Capacity and Weight. 1. OF GREAT BRITAIN.* The denominations are pounds, shillings, and pence. EXAMPLES. 1. What is the amount in Federal Money of a Bill of Exchange on a merchant at Liverpool of £133 sterling, sold in New York at per cent. advance ? £ $ c. 133591.11 2.9510 per cent. Amount $594-06 Ans. 2. In Aug. 1821, Bills on London, bore at Boston a premium of 81 per cent.; what is the amount of a bill of exchange of £250, at this rate, in Federal Money, and what is the value of a pound sterling at this course of exchange? Ans. Amount $1205 55 cts. Value of a pound sterling $4 32 cts. 3. A Bill of Exchange on London of £90 sterling, was sold at New York, at 36 shillings New York currency per pound sterling; what was its amount in the currency of New York, and how much above or below par? £ S. £ £ As 1 : 36: 90 : 162 N. Y. currency. Now £9 sterling £16 N. Y. currency, or 20s. sterling-35 N. Y. currency. But 36-35-4s. N. Y. currency, the gain on every pound sterling, or £2 N. Y. in the whole. Then, as 35gs.: :: 100: 14 per cent. above par. Or, 162-2: 2 :: 100: 14 do. 4. The invoice of goods, amounting to £170 10s. sterling, is sold at New York at 25 per cent. advance ;t what is the amount in Federal Money? Ans. The Rules on which the operations of Exchange are performed, are obvious from the rules for Reduction of Coins, and the Rule of Three. + To reduce sterling money to the currency of New England, when there is a certain per cent. advance, merchants use the following method. For 12 per cent. advance, multiply the sterling by 14 20 25 314 50 621 873 100 125 150 175 200 13 13 31 These multipliers are thus formed. Let the advance be 25 per cent. on £100; then, as 25 of a hundred, 100x 100 500 the sum with the advance. This is to be reduced to New England currency by increasing it by one third of itself. 1663 pounds; which is evidently the same as to mul tiply 100 by 13. In the same way may the other multipliers be found. 5. A Bill of Exchange of £75 16s. is sold at Boston at 26s. New England currency per pound sterling; what is the value in Federal Money of a pound sterling at this rate of exchange? Ans. 2. OF FRANCE. The money of account is livres, sols, and deniers. 12 deniers make 20 sols 1 sol or shilling. 1 livre or pound. The livre is estimated at 184 cents in the U. S. The crown of exchange is 3 livres, or livres tournois, and is equal to 55 cents. The present money of account is francs and centimes or hundredths. 80 francs 81 livres, or a franc=1 livre. 1. To reduce francs to livres, or the contrary, multiply the francs by 81 and divide the product by 80 for livres; or multiply the livres by 80 and divide the product by 81 for francs. 2. To reduce livres to dollars and cents; multiply the livres by the cents in a livre at the course of exchange. EXAMPLES. 1. If the livre be 20 cents in exchange, what is the amount of 2150 livres in Federal money, and what is the per cent. above par at this exchange? Ans. Amount is $430. And above par 8 per cent. 2. If the livre be 18 cents in exchange, required the amount of 3580 livres 16 sols, in dolls. and cents, and the rate per cent. below par. Ans. 644-54 cents, and 234 per cent. below par. 3. If a crown be valued in exchange at 18d. sterling, required the livres in £100 sterling, and the amount also in Federal money d. liv. £ liv. at par. As 3 livres 1 crown, 18: 3 :: 100: 4000 and 4000×1813740. 4. In 2583 francs, how many dollars? 2583×551=1433dolls. 564 cents. 5. A bill of exchange on a merchant in New York of $730 65cts. was bought at Paris at 1 per cent. advance; what is the amount in francs, and what was the estimated value of a franc at this, exchange? Ans. 1 piastre or current dollar. 1 ducat of exchange. Hard or plate dollars are 88 per cent. above current dollars or money of vellon, or |