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2. Required the present worth of dols. 9356,25, for 2 years, and 5 months, at 5 per cent. per annum.

Ans. dols. 8347,59,3+ 3. What is the present worth of 4000 dols. payable in 9 months, at 4,75, or 4 per cent. per annum?

Ans. dols. 3862,40,1+ 4. Suppose 810 dols. were to be paid 3 months hence;, allowing 5 per cent discount, what must be paid in hand, or at the present time ? Ans. 800 dols.

5. If a legacy be left me July 24, 1808, to be paid on the following Christmas day, what must I receive when I allow 6. per cent. per annum, for present payment, the legacy being 1000 dols. Ans. dols. 975,15,3+

6. Being obliged by note, dated August 29, 1807, to pay on the 24th of June, 1808, (which is 'leap year,) £326, what must I pay down if I am allowed a 'discount at the rate of 8 per cent. per annum ?

Ans. £305,16,6{+ When goods are sold, and payment to be made at different times, to find the discount or present worth of the whole.

RULE. Find the discount or present worth of each payment for its time, and add them together, their sum will be the discount, or the present worth of the whole.

This is the truest and most accurate method, but the discount or the present worth of several payments may be found very near the true sum, by finding the equat ed time, and then use that time, as if it had been a time given to pay the whole.

By this last method the discount will be greater, and the present worth less than by the true method ; the seventh example by this last method gives the present worth dols. 3062,57,6+ but the true present worth is dols. 3062,69,6+ Also, the eighth example, instead of the true present worth, dols. 296,06,1+ would be dols 296,05,2+ by this last method ; the ninth example, instead of dols. 975,67,4+ would be dols. 975,60,9; the tenth example would be dols. 198,01,9+ instead of dols. 198,02,2+

NOTE. When the sums are large, the true method ought always to be preferred. When no time is mentioned, a year's interest is the discount.

7. Sold goods for dols. 3120, to be paid in two 3 months, (that is, half at 3 months, and the other half at 3 months after that,) what must I receive present payment, if I allow a discount at the rate of 5 per cent. per annum ?

Ans. dols. 3062,69,6+ 8. Sold goods for 300 dols. to be paid at three 2 months, (that is į at 2 months, į at 4 months, and į at 6 months) what must I receive for present payment, if I allow a discount at the rate of 4 per cent. per an. num ?

Ans. dols. 296,06,1+ 9. What is the present worth of 1000 dols. payable at two 4 months, discount 5 per cent. per annum ?

Ans. dols. 975,67,4+ 10. What is the present worth of 200 dols. at 4 per cent. per annum discount, payable 100 dols: at 2 months, 50 dols. at 3 months, and 50 dols. at 5 months ?

Ans. dols. 198,02,2+

Bank Discount.

Bankers find the interest of the sum, from the date of the note, to the time of payment, including the days of grace ; this interest is called the discount ; i. e. if a note, dated the 1st of August, 1809, be discounted at a bank for 30 days, the interest of the note for 33 days is the discount, if 3 days of grace are allowed ; because the borrower can with hold the payment for 33 instead of 30 days.

When a new note is given (on account of its being inconvenient to pay at the specified time) it must be presented on the day of discount immediately preceding the expiration of time of payment specified in the note, paying the discount as before, for the time.

If a note of 100 dols. dated August 1, 1809, for 30 days, though it is not payable till the 2d of September, (yet if not paid) a new note must be replaced on Tuesday, the 29th of August, (if Tuesdays are the days of discount, and no other day in the week) paying discount as before, for the time it is to bear interest, including the days of grace.

The usual method of finding the discount in banks for 30 or 60 days is, by multiplying the sum by one sixth part of the days, (including the days of grace,) and pointing off 3 places of the right hand figures, those at the left of the point will be dollars, if dollars only are multiplied. If dollars and cents, or dollars cents and mills, or cents only, or mills only, are multiplied ; after pointing off the three right hand figures from the product, the others will be of the same denomination, with the lowest multiplied.

Always take a sixth part, the given days increased by three, i. e. if 30 days, take for 33, if 60 for 63, &c.

EXAMPLES. 1. How much must be discounted for a note of 476 dols. at 30 days?

476
6)33 (=51 multiplier.

2380
238

dols. 2,61,8 Ans. 2. How much is to be discounted for a note of 438 dols. at 60 days?

438
6)63(=104

4380
219

dols. 4,59,9 Ans. Note 1. In these examples three days of grace have been calculated for.

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NOTE 2. If the unit figure in the dollars given is 1, 3, 5,7 or 9, there will be one half mill in the discount.

Dollars. For days. Discount. 3 477

dols. 2,62,2 4 4388

30

24,13,4 5 7365

30

40,50,71 367

30

2,01,84 7 1372

60

14,40,6 8 9327

60

97,93,31 9 865

60

8,93,21 10 1572

90

19,65 11 423

90

5,2837 | 12 7645

90

95,56,24 13 372,45

30

2,14,8,475 14 564,36

30

3,10,3,98 i, 15 583,55,4

30

3,2 1,4,547 16 436,57

4,58,3,985 17 473,17,5

60

4,96,8,3375 18 597,36,9

90

7,46,7,1 125 Nore. In the six last examples 'the decimals of a mill are inserted for the satisfaction of the pupil. * 1)

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Exchange is the giving the bills, money, weight, or measure of one place or country, for the like value in the bills, money, weight, or measure of another place or country ; in doing which it is necessary to know how to change any sum of money, or any weight, &c. of one place or country, to a sum or weight, &c. of another country, or place, of equal value.

This is done by finding what proportion a certain sum of the money of one country or place, bears to the like, sum of the money of the other country or place, and using these proportional numbers as follows, viz.

1. If the given sum or weight be of more value than a like sum or weight in the place required,

Multiply it by the greater of these proportional numbers, and divide the product by the less.

2. If the given sum or weight be of less value than a like sum or weight in the place required.

Multiply the given sum or weight by the less of these proportional numbers, and divide the product by the greater, the quotient in either case will be the sum or weight required, of equal value with that given.

Questions in Exchange may be proved by varying their order.

Note. In many instances the money or weight of one place may be changed to that of another by adding to, or subtracting from the given sum or weight, a certain proportion, as in many of the following examples.

To change the currency of New England and Virginia to Federal money.

CASE I. When pounds only are given, annex a cipher, and then divide by 3, the quotient will be dollars ; if any remains, annex to it two ciphers, and then divide by 3 for cents ; if there is still a remainder, and you wish to know the value to a lower denomination, annex one cipher and divide by 3 for mills.

Case II. If pounds and shillings are given.

When the number of shillings given is even, as 2, 4, &c. annex half their number to the pounds, and divide by 3, &.c. as above.

If the number of shillings given be odd, as 1, 3, 5 &c. then after annexing half the greatest even number of shillings to the pounds, annex 50 ; and divide by 3 gives cents. If there be a remainder, annex a cipher, and divide by 3 for mills.

CASE III. If pounds, shillings and pence, &c. are given.

Proceed as in the last cases with the shillings, and then add a number equal to the farthings, the pence farthings will make, increased by one, if they make more than 12, and not more than 37 ; but if more than 37 increase it by 2, then divide by 3 gives cents ;. if any remains, annex a cipher to it, and divide by 3 gives mills.

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