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52. In what time will 100 dollars, or any other sum of money, double itself, at 6, 7, 8, or any other rate per cent. per annum, simple interest?

Rule. As the rate per cent, is to one year, so is 100 dollars to the number of years it will be in doubling itself; or, divide 100 dollars by the rate per cent. and the quotient is the time.

EXAMPLES.

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year. $
As 6 1 :: 1009

16 years.
7 1
100

144
8 1
100

12)
Ans. 163 years at 6 per cent. 144 years at 7

per

cent. 12 years at 8 per cent. and $100, at 5 per cent.

will be 20 years in doubling itself. 53. In what time will 340 dollars 25 cents amount to 626 dollars 6 cents, at 7 per cent. per annum ?

Ans. 12 years. 54. In what time will 650 dollars amount to 910 dollars, at 8 per cent. per annum?

Ans. 5 years.

A TABLE shewing the number of days, from any day in

any month, to the same day in any other month, throughout the year.

Jan]Feb]Mar]Apr]May]June]July ]Aug]Sept]Oct]Nov] Dec Jan.

365 , 334 : 306 1 275 245 -274 184 153 122 92 61 31 Feb. 31 365 337 306 276 245 215 184 153 | 123 92 62 March 59 28 365 334 304 273 243 212 181 151 | 120 90 April

90 59 31 365 335 304 274 243 212 182 151 121 May

120 i 89 61 30 365 334 304 273 242 212 181 151 Jane

151 | 120 92 61 31 365 335 304 273 243 212 182 July 181 150 122 91

30 365 334 303 273 242 212 Aug. 212 181 | 1531 122 92 61 31 365 334 304 | 273 343 Sept. 243 212 184 | 153 123 91 62 31 365 335 304 274 Oct. 273 242 214] 183 153 122

61 SO 365 334 304 Nov. 304 273 245 214 184 153 123 92 61 91 365 335 Dec. 334 30375 244 214 183 153 122 91 161 30 365

92

Use of the Table.-Suppose you want to know the num. ber of days between the 8th of May, and the 8th of November following. Under the column of May, at the top of the table, look for November in the left-hand column, and you will have 181 days.

Again, how many days from the 4th of March, to the 4th of September following? Look in the top column for March, and in the left-hand column for September, and run your finger along, until you come to the column headed March, and you will find i84 days. , And if it be required to find how many days there be from 14th June, to the 20th April, you must find how many days there are, first from the 14th of June to the 14th of April, which you will find to be 304 days; then add the number of days from the 14th to the 20th June, which is 6, to 304, and it will make 310 days. If the days in the given months be different, their difference must be added to, or subtracted from the number found in the table. Thus, from the 14th of June to the 20th of April, is 304+6=310 days; and from the 20th April to the 14th June, is 61 days, less 6, equal 55 days. If the time exceeds a year, 365 days must be added for each year.

Calculating interest on bonds, notes, &c. RULE 1. Find the interest of the principal from the time the interest first commenced, to the time of the first payment, and add the interest thus found to the principal, and subtract from the whole the payment made, and the remainder forms a new principal, on which proceed as you have done, till all the payments are brought in. By this rule, when a payment alone, or in conjunction with any preceding payment, is less than the interest then due, no calculation is to be made, but these lesser payments added to the next. Therefore no part of the interest ever forms, or becomes a part of the principal bearing interest, the pay. ments being first applied to discharge the interest.

There are other methods used, which I will give examples of; but the above one is the best.

EXAMPLE.

55. A passed his note to B for 800 dollars, dated the first of January, 1823, payable in four years, with interest from the date, at 6 per cent. per annun, on which A paid the following sums, viz.

1823, July 1st, paid on said note $100
1823, Nov. 1st, paid
1874, Jan. 1st, paid
1824, Sept. 1st, paid
1825, Sept. 1st, paid
1826, April 1st, paid

150

$ 680 paid. What was the balance due on A's note, on the first day of January, 18277

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150 100

80 100)

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Principal at interest from Jap. 1st to July 1st, 1823
Six months interest

$80000

24.00

Due first of July
Paid same date

824 00 100 00

Balance due, the new principal
Interest'on said balance, up to 1st Nov. (4 months)

724 00 14 48

Due first of November
Paid same date

738 48 150 00

588 48
5 88+

The new principal, bearing interest
Interest on said balance, up to Jan. 1st, 1824, (2 months)
Due first of January, 1824
Paid same date

594 36 100 00

O

The new principal, bearing interest
Interest on said new principal, to Sept. 1st, (8 months)

494 36 1977+

Due first of September, 1824
Paid same date

514 13 8000

The new principal, bearing interest

434 13 Interest on said new principal, to Sept. 1, 1825, (12 months) 26 04+

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360 17
12 61+

The new principal, bearing interest
Interest on said new principal, to April 1, 1826, (7 months)
Due first of April, 1826
Paid same date

372 78
150 00

The new principal, bearing interest

222 78 Interest on said new principal, to Jan. 1, 1827, (9 months) 10 02+ Due first of January, 1827

$ 232 80 NOTE. I did not bring in the fractions.

Another method, used by merchants. RULE 2. Multiply the principal by the number of days, till the first payment is made, and the remaining principal by the number of days between the first and second pay. ments, &c. till all the payments are made; then add all these products together, and divide the whole sum by 60, and the quotient will be the answer, or interest in cents. This divisor 60 will do when the rate is at 6 per cent. This 60 is found by dividing 6 into 365 days. A divisor for 5 per cent. is found by dividing 365 by 5=73, &c.

The above question performed by this rulet

dolls. days.

days. 8 ota. 1823, Jan. 1st, Principal 800x181-14480023 80 July 1st, Paid

100

Balance 700X123= 86100 14 15+ Nov. 1st, Paid

150

Balance 550X 61= 33550 5 51+ 1824, Jan. 1st, Paid

100

Balance 450 X 243 = 109350 17 97 + Sept. 1st, Paid

80

Balance 370x365=13505022 20+ 1825, Sept. 1st, Paid 100

Balance 270x212= 57240! 9 40+ 1826, April 1st, Paid

150
Balance 120x275= 33000 5 42+
Interest 98 45

599090/98 45
Amount due $ 218 45
60)599090

Balance $12000

Interest 99 84+ 9984 + cts.

Amount due $ 219 84 NOTE. The column above, containing the interest of the several balances is calculated by Compound Proportion. The divisor 60 is not correct, bem cause 365 divided by 6 gives 605 as a quotient. But multiply 365 days by 100 dollars 36500 – 6 – 6083+ for a divisor, which will give the quotient in dollars. Thus,

6083)599090

98 48+ interest.
120 00 balance,

Amount due $ 218 48

RULE 3. As 100 dollars, with 365, is to 6 per cent, 80 is the different balances, with their number of days, to their respective interests.

RULE 4. Multiply the number of days into the balances at interest, add their products together, and divide that sum by 6083, and the quotient will be the answer in dollars, that is, the interest, which, added to the balance of principal due, will be the whole amount due.

Another method.

Rule 5. When the time is months, or months and days between each payment, multiply each sum by the months it is at interest, and take the quotient of 1200, divided by the rate per cent. as a divisor. Thus, for 6 per cent. the divisor is 200, for 5 per cent. 240, for 8 per cent. 150, &c.

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New principal

550 X

2 = 1100
Paid Ist Jan. 1824 100
New principal

450 X

8 5600
Paid 1st Sept. 1824 80
New principal

370 X 12 4440
Paid 1st Sept. 1825 100
New principal

270 X

7 * 1896 Paid ist April, 1826 150 Balance up to Jan. 1, 1827 120 X 9 = 1080

200) 197 10

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RULE 6. Find the interest on the principal, from the time the interest commenced, to the time of settlement, and add it to the principal, and likewise the interest on each payment, from the time the payment was made, to the time of the settlement, and add the several interests to their respective payments, and deduct the whole amount from the amount of the note, bond, &c. and the remainder is the balance due on the note, &c.

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