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5. A man bought a quantity of goods, to pay { at the end of every 3 months, till the whole was paid ; but it is

3 agreed to make one payment of the whole. Required the equated time.

Ans. 6 months. 6. A debt of 420 dols. is due at the end of 6 months, but the debtor will pay 60 dols. now, provided the rest may be forborne a longer time, which is agreed on. Required the time.

dols. 430 Paid present,

60

months. Remains,

360 :: 6 :: 4.20

6

360)25270(7 months, Ans.

252

Note. In the 6th example, it is evident that if part is paid now, the remainder ought to be forcorne a longer time. See the stating, agreeably to the general method of stating the Rule of Proportion:

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Discount is an allowance made for the payment of a sum of money before it becomes due, and is the difference between the sum due, at a time to come, being specified and the sun which ought to be paid at the present time, (called the present worth) which is put to interest would amount to the given sum at the time specified.

Discount is also sometimes allowed on depreciated money, such as foreign coin, the bills of some banks, &c ; in this case it is commonly at so niuch per cent ; in the former case so much per cent. per annum.

CASE I. To find the discount on a sum of inoney payable on a future day,, provided the same be paid at the present time ; the sun and rate of discount being given.

RULE 1. As 12 months, or 365 days, are to the rate per cent, so is the time proposed, to a fourth number, or sum.

2. Add that fourth number, or sum, to 100 pounds, or 100 dollars, (as the given sum may be.)

3. As this last sum is to the fourth number, so is the given sum to the discount.

EXAMPLES. 1. Required the discount of £795 11 2, for 11 months, at 6 per cent. per annum ? 12 : 6 :: 11

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2. What is the discount of dols. 9356,25, for 2 years and 5 months, at 5 per cent. per annum ?

Ans. dols. 1008,65,6+ 3. What is the discount of dols.-957,26, for 7 months, at 6 per cent. per annum ? Ans. dols. 32,37,17

CASE II. To find the present worth of a given sum, payable at a future day, having the rate per cent given.

RULE. Proceed as directed in Case I, till the fourth number or sum is found and added to 100; then say, as that sum is to 100, so is the given sum to the present worth ; or, find the discount as directed in the ist Case, and subtract it from the given sum; the remainder will be the present worth.

EXAMPLES. 1. Required the present worth of £795 11 2, for 'li months, at 6 per cent. per annum.

6 12 : 6 :: 11

11
12)66
5 5 or 65 10

100
105 10 : 100 :: 795 11 2
20

20
2110

15911 12

12
25320 190934

100
2532|0)190934010(£754 1 89 6. Ans.

17724 This proves the first example in

13694 Case 1.
12660
10340 Or, thus, From
10128 the given sum £795 11 2
212 Subtr. discount,

20 Found by Case I 41 9,54
4240 Example 1,

present worth, 1708

754 1 890 12 20496 20256

240

960

2332

2532 Remains the

2632

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 44 per cent. per annum?

Ans. dols. 3862,40,1+ 4. Suppose 810 dols. were to be paid 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 equated 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 dois.

the tenth example would be dols. 198,01,97 instead of dols. 198,02,2+

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NOTE. When the sums are large, the true method ought always to be preferred. When no time is mentioned, a year's interest is ihe 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 at 2 months, at 4 months, and fat 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+

a

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 withhold 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.

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