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25. A railroad has been constructed through a farm, in consequence of which, the owner of the estate is obliged to expend $400 in fencing, that must be renewed at the expiration of every 12 years. What sum should he now receive, to compensate him for the required expenditure, money being worth 6 per cent, compound interest ?

PROBLEM IV.

The present worth of a certain annuity being given, to find the annuity.

RULE.

Find the first term of a Geometrical Progression, in which the sum is the amount of the annuity for the whole time, the ratio is the amount of $1.00 for the time that elapses between two successive payments, and the number of terms is the number of payments.

26. The present debt of Pennsylvania (in 1844) amounts to about $40000000, which bears an interest of 5 per cent. per annum, payable semi-annually. What semi-annual appropriation will extinguish the debt in 40 years ?

27. What sum of money must a man lay up annually, to amount to $10000 in 20 years, the investments being all made at 6 per cent. compound interest ?

28. A builder takes a lease of a lot of ground for 25 years, and erects buildings on it which cost him $20000. Allowing money to be worth 6 per cent. compound interest, what clear* annual rent must he receive from the buildings to reimburse his expenditure, at the termination of the lease,—the rent commencing one year after the lease is given ?

29. The executors of an estate wish to dispose of an unexpired lease that has 8 years to run, for a premium of $1500. What amount must be added to the annual rent, for that purpose ?

* The clear annual rent, is the amount received after deducting ground-rent, taxes, and other expenses.

PROBLEM V.

To find the present worth of an annuity in reversion.

RULE.

Find the present worth of the annuity until the commencement of the reversion, and also the present worth until its termination. The difference of these two values will give the present worth of the reversion.

30. What is the present worth of an annuity of $1100, to commence in 3 years and continue for 8 years, interest at 6

per cent ?

31. What is the present worth of a perpetual annuity of $300, to commence in 2 years, at 5 per cent. interest ?

32. A father leaves an annual rent of $400 to his eldest child for 5 years, and the reversion of it for the 8 succeeding years to his youngest child. What is the present worth of each legacy, at 7 per cent. ?

33. What sum must be paid, allowing 6 per cent. compound interest, to extend a lease 7 years,—the clear annual rent being $500, and the lease having 4 years to run

? 34. What is the value of $3000 rail-road stock, that will yield no income for 4 years, but on which, after that time, there will be an annual dividend of 9 per cent. for 21 years ?

35. What is the present worth of a reversion of $700 per annum, to commence in 20 years, and continue 40 years thereafter, allowing 6 per cent. compound interest ?

The operations in annuities are generally so tedious, that tables similar to those given at the end of the book, are employed in their calculation.

The subject of LIFE ANNUITIES, involves the calculation of chances, as applied to the duration of life. Tables of the probable duration of life at each year, are prepared, and the number against each age is employed as a multiplier or divisor, for determining the present worth, or the annuity itself.

CHAPTER XXI.

EXCHANGE. The term Exchange in commerce, is generally employed to designate that species of mercantile transactions, by which the debts of individuals residing at a distance from their creditors, are cancelled without the transmission of money.

A BILL OF EXCHANGE is an order addressed to some person at a distance, directing him to pay a certain sum to the person in whose favor the bill is drawn, or his order. The person who draws the bill, is called the drawer ; the person in whose favor it is drawn, the remitter or payee ; the

person on whom it is drawn, the drawee. The drawer is also called the acceptor, when he has accepted, or engaged to pay the bills.

Though Bills of Exchange are originally drawn by credi. tors on their debtors, they are very rarely transmitted directly, but pass from hand to hand like any other circulating medium, and are bought and sold in the market. When the remitter disposes of a bill, he writes his name on the back, and is termed the indorser. If he indorses in favor of any particular individual, he gives a special indorsement, and the indorsee must also indorse the bill if he negotiates it. But if the indorsement is blank, the bill may be passed at pleasure from hand to hand. Every indorser, as well as the acceptor, is held responsible for the payment of the bill, and may be sued for its recovery.

INLAND, or DOMESTIC EXCHANGE, includes the commercial transactions within the limits of one country. Foreign ExCHANGE relates to the transactions of one country with another.

The True Par of EXCHANGE is the value of the currency of one country estimated in the currency of another, by comparing the quantity of gold and silver in their respective coins. The exchange with England apparently furnishes an exception to this rule, the nominal par being $4.444 per £, while the actual value of the pound sterling, which is the

real par, is about $4.87. Hence exchange on England is generally said to be from 8 to 10 per cent. above par.

The COURSE OF EXCHANGE, or the fluctuation above or be. low par, depends generally on the amounts due between dif. ferent countries. Thus when the debts and credits between two countries are equal, the real exchange is at par. But if New York owes London more than London owes New York, there will be a greater demand for bills on London, and this demand will produce a rise in the price, or cause the bills to be at a premium The premium, however, can never exceed the cost of transporting specie ; for if it did, all debts would be paid in money or merchandise, instead of bills of exchange. The nominal premium, however, may exceed the cost of remitting coin, when the nominal par is above the

real par.

The operation of Bills of Exchange, may be explained by a single example.

If A. of Boston, owes B. of Paris, and C. of Paris owes D. of Boston, A. purchases in the market a bill upon Paris ; that is, he buys of D. an order on his creditor C., to pay A. or his order, the amount desired. A. indorses the bill, and sends it to B., who receives payment from C. Thus the two debts are cancelled by a single remittance; the inconveni. ence of exporting and re-importing coin is removed, and all danger of loss is obviated, by sending three bills, (called the First, Second, and Third of Exchange, either of which being paid the others are void.

An ACCEPTANCE is an engagement to pay the amount of the bill, and may be either absolute or qualified. An absolute acceptance binds the drawer when the bill becomes due, and in making it, the drawee usually writes - Accepted," and subscribes his name at the bottom, or across the body of the bill. A qualified acceptance implies some condition, as the sale of merchandise, &c., and does not bind the acceptor until the condition is complied with. If a bill is made payable at a certain time after sight, the acceptance should be dated.

A bill should be presented for payment during the regular hours of business, on the day it becomes due.

When acceptance or payment has been resused, the holder should give immediate notice to all the parties whom he in

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tends to hold responsible for the payment of the bill. This notice is usually accompanied with a Protest, which is an instrument prepared by a public notary, stating that acceptance or payment has been demanded and refused, and that the holder of the bill intends to recover any damages which he may sustain in consequence.

In some places on the continent of Europe, banks of deposite are established, and exchanges are frequently made by transferring the amounts credited on the books of the bank from one person to another. The deposites on which these credits are based, are called banco, and they usually bear a premium above the ordinary currency of the country. This premium is called the agio.

The comparative market value of gold and silver is constantly varying, and the mint value is differently estimated by different governments. Thus, in England the relative worth of the two metals is as 1 to 14.29, in France, as 1 to 15.52, and in the United States, as 1 to 15.99. In England, silver is so much overvalued, that it would banish the gold coins from circulation, were there not a statute providing that gold only shall be legal tender in all payments of more than 40 shillings. The relative value of the precious metals should always be considered, in estimating the true par of exchange with any country.

DOMESTIC EXCHANGE.

Inland Exchange is usually effected by checks or DRAFTS, similar in form to the following: $1275.25

Philadelphia, June 3, 1844. Sixty days from date, pay to James N. Lewis, or order, Twelve Hundred and Seventy-Five Dollars and Twenty-Five Cents, and charge the same to my account.

William Morris. To Markham & Jones,

Merchants, Cincinnati. The premium or discount on drafts, may be owing either to a difference in the value of the circulating medium, or to fluctuations in the demand. The English denominations of shillings and pence, are

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