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21. Find the discount to be allowed on the following bills, discount as interest, at 6 per cent per annum ?

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22. What is the present worth of the following 6 bills, discount as interest, at 6 per cent per annum; the first 1701. 10s. payable in 32 days, the second 1451.4s. 8d., payable in 37 days, the third 120l 16s. 3d. payable in 45 days, the fourth 110l 13s. 4d. payable in 79 days, the fifth H50l 15s 0d §. in 43 days, and the sixth 133l 12s. 6d. payable in

days : , To find the true present worth, or discount of any sum, payable at any time to come, the following is the rule —

As 100 with its interest for the given time, added thereto, is to the sum to be discounted, so is 100, to the present worth required. And this present worth subtracted from the debt, gives the discount. Or, as 100 with its interest added thereto, is to the given sum to be discounted, so is the interest of 100l, to the true discount; and this discount subtracted from the debt, will give the true present worth, the same as if the former rule had been employed.

Čpamples. ..

23. What is the true present worth of a bill for 1481, due at the end of 3 months, at 6 per cent, per annum ?

The interest of 100l for 3 months, is ll 10s. 0d,

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24. what is the true present worth of a bill of 78! 15s. 0d. due on the first of August, but paid on the 5th of June preceding, at 6 per cent per annum ? .

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25. What is the true discount of a bill of 2151, drawn on the 1st of March, at 6 months, and discounted on the 7th of June, at 5 per cent per annum ?

Here the number of days is 89.

89 356=days x4 70)85,44 1,2265 Correction, 1 Interest of 100l for given days, 1,2195 se-

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Should it be thought necessary for the Pupil to calculate discount. torrectly, the eramples already given will be sufficient for the purpose, and by working those both ways, he will see the comparative advantages and disadvantages of the two methods, ,

EQUATION OF PAYMENTS:

Equation of payments, is the finding of a time to pay at once several debts due at different times to come, so that neither the holder nor receiver should suffer loss.

Rule.—Multiply each payment by the time when it is due, and divide the sum of these products by the sum of the payments, the quotient is the equated time sought. o

Proof–If the interest of the sum of the payments for the equated time, be equal to the sum of the interest of the separate payments, the work is right.*

* I am aware that some have questioned the mathematical accuracy of the above rule; but for a demonstration, and other observations. *reo; I refer the reader to John Walker's Philosophy of Arithunetic, Pages 63 and 64,

Corampled. 1. A merchant sells goods belonging to his correspondent, as follows : to A. to the amount of 275l, payable in 3 months, to B. 2001, payable in 1 month, and to C. 254l, payable in cash : at what date ought his correspondent to draw in one. sum for the whole, allowing each month 30 days?

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2. A. owes B. 25l payable in I month, 30l payable in two months; 45l to be paid in 3 months, and 15l to be paid in 4 months; what is the equated time for the payment of the whole?

3. A. purchases goods from. B. on the 15th of January, amounting to 275l; on the 1st of February, to the amount of 125l ; on the 10th of March, to the amount of 312! ; he is allowed 3 months credit on each purchase, but wishes to give B. a bill for the whole, at 31 days date; when should it be dated, it being a common year?

4. Received invoice of sundry goods to sell for account of A. B. which I disposed of as follows:—

To A. to the amount of 1501 payable in 91 days.

To B. . . . . . . . . . . . . . of 175l payable in 61 days.
To C. . . . . . . . . . . . . . of 200l payable in 124 days.
To B. . . . . . . . . . . . . of 180l payable in cash.

At what rate ought A.B. to draw on me in one bill for the whole * 5. Suppose a debt is to be discharged thus, 3 at present, +,

in 31 days, # at 61 days, and the remainder in 91 days; what

time may the whole be paid at once?

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6. Suppose I have received at Jimerick the following bills, all payable in that city; 1001 due in 4 months, 2001 at 3 months. 150l at 2 months, and 250l at 1 month, and agree to pay a banker there, a reasonable commission and expense of stamp : at what date ought he to give me a bill on Dublin for the whole.” 7. Suppose I owe 300l to be paid in 3 months, but am willing to pay 120l down, provided the time of payment for the remainder of the debt is lengthened in proportion, and that my creditor agree thereto —the time is required :

8. What is the just time for the payment of 3 debts, the first 2391 12s. 6d. the second of 1471 17s.6d. and the third for 280l 10s. ; the first due in 9 months, the second in 15 months, and the last in 23 years?

9. If a debt of 1000l be payable one half in 6 months, one fourth in 8 months, and the remainder in 12 months; what is the equated time for the payment of the whole P

ExCHANGE.

Exchange is the bartering or exchanging the money of one place or country for that of another, by means of bills of exchange, orders for the payment of money, or the removal of money from one country to another, and is comprehended in this problem, how much of one country's money is equal in value to a certain sum of another country's money, at a given rate or proportion.

The par of Exchange between two countries is the intrinsic value of the money of one compared with that of the other.

The course of exchange is the value agreed upon by merchants or their factors, and is continually fluctuating above or below the Par of Exchange, according as the demand for bills is greater or less. w

All calculations in Exchange may be performed by the rule of proportion, and the operation may be often abbreviated by means of aliquot parts and other devices.

In Foreign Exchanges, one place always gives another a fixed sum or price, to receive an undertimed one.

Merchants and traders in Ireland, for the most part, have no direct exchange with any other place, therefore, exchange between England and leeland, and the contrary, would be sufficient for the generality of them; yet, as they draw their Foreign demands by way of London, I have given the mode of calculating exchange, not only between Great Britain and Ireland, but also between that country and a few other places of most general intercourse,

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