this product divided by 200, will give the INTEREST of that sum for that time, at 6 per cent.; hence,

I. To calculate interest at 6 per cent., we may observe this

RULE.

First. Multiply the principal by the number of months, and divide the product by 200; or,

Second. Multiply the principal by the number of days, and divide the product by 6000; in either case, the quotient will be the ANSWER.

II. To calculate interest for ANY time and rate per cent., observe this

General RULE.

MULTIPLY the principal by the days in the time, and the rate per cent., and divide the product by 36000, the quotient will be the ANSWER.

EXAMPLES.

1. What is the interest of $846.50 for 11 months, at 6 per cent.?

Thus:

84650 11 931150 Dols.

NOTE. In this example the principal is represented as so many hundredths of a dollar, and expressed in the form of a vulgar fraction; 11 months are placed above the line, and 200 below the line, we then multiply $84650 by 11, making 931150 for the dividend; second, multiply 100 by 200, making 20000 for the divisor; and, lastly, we divide 931150 by 20000, giving $46.553. Answer.

2. Required the interest of $7648.87 for 7 months, 17 days, at 6 per cent. PER ANNUM?

3. Required the interest of $5685 for 3 years, 5 months 13 days, at 3 per cent, PER ANNUM,

In this example we have 1243 days' interest, at per cent.; hence, according to the GENERAL RULE, we must multiply $5685 by 1243, and by 7, and divide by 36000, and by 2, i. e., by 72000. In every case where either of the above RULES are practised, the learner should draw a line lengthwise, as in the examples, and then inspect the quantities, placing such factors as will produce the DIVIDEND above, and those which will give the DIVISIOR below the line; then cancel as much as possible, and find the product of each class of factors, after which, divide for the ANSWER.

QUESTIONS FOR EXERCISE.

1. What is the interest of $436.50 for 3 months, at 6 per cent.?

2. Give the interest of $976.84 for 5 months, at 6 per cent.? 3. How much interest will $25000 draw in 15 months, at 6 per cent.? how much in 17 months?

4. What is the interest of $3450 for 27 days, at 6 per cent.? 5. How much interest will $9685 draw in 1 month, 25 days, at 6 per cent.? how much in 3 months, 20 days?

6. What is the interest of $1262.50 for 2 months 19 days, at 6 per cent.?

7. What interest would accrue from $20000000 in 1 day, at 6 per cent.? what would be the income of 1 hour?

8. What is the interest of $4682, for 23 days, at 5 per cent.? at 3 per cent.? at 4 per cent.?

9. What is the interest of $432.25, from the 15th of January, 1820, to the 10th of October, 1821, at 7 per cent.?

NOTE.-When interest runs from one date to another, we should find the time by subtracting the dates, as on page 159. When a note is given on time, we should first find the whole time, as above, and from THIS subtract the time which the note has to run before it becomes due, the remainder will be the time for which INTEREST must be found.

10. What is the interest of $425.621, from the 18th of February, 1825, to the 15th of March, 1828, at 51⁄2 per cent.?

11. I gave a note, dated 16th of April, 1828, for $450, and paid it on the 4th of May, 1829, allowing interest at 6 per cent., for the whole time, what did the note AMOUNT to, how much money would be required to pay it?

i. e.,

NOTE. To obtain the amount, it is only necessary to find the interest, and add it to the principal.

12. How much cash will discharge a note for $325.50, dated Jan. 20, 1830, and paid, Oct. 15, 1835, at 6 per cent. ?

13. What is the interest on a bond, for $745.54, dated June 24th, 1836, and paid April 9th, 1840, at 7 per cent.?

14. How much money will cancel a note for $675.62, dated April 10th, 1814, and paid, August 15th, 1820, due in 6 months, interest at 4 per cent.?

INTEREST ON BONDS, OR NOTES.

When a BOND, or NOTE, is not due for a considerable time hence, and partial payments are made at different periods, it becomes necessary to guard against the payment of illegal or compound INTEREST, to prevent which it has been customary to find the AMOUNT of the bond or note, up to the time of the first payment, which having been taken from IT, the remainder draws interest to the time of the second payment, &c., by which course it is plain, that if any partial payment, is less than the interest up to the time it was made, that part of the interest not cancelled, will form a part of the principal, and therefore, draw interest till the next payment is made, thus creating COMPOUND INTEREST, to prevent WHICH we may adopt the following

RULE.

First. FIND the AMOUNT of the BOND or NOTE, from the date thereof to the time of SETTLEMENT.

Second. FIND the AMOUNT of each PAYMENT from the date at which such PAYMENT was made, to the time of final SETTLEMENT; and,

Third. SUBTRACT the SUM of these several AMOUNTS of PAYMENTS from the AMOUNT of the BOND, already found, the REMAINDER, if any, will be the BALANCE, or last PAYMENT.

EXAMPLES.

1. A NOTE, dated April 4th, 1840, was given for $560 with interest from date, at 6 per cent. PER ANNUM, on WHICH the following payments were made: 1st. Dec. 12th, 1841, $125; 2d. May 8th, 1842, $75; 3d. June 6th, 1843, $150; 4th. Sept. 6th, 1844, $50; how much remains due on the 16th of August, 1845? Thus :

Amount of NOTE for 5y. 4mo. 12 days=
Amount of first payment for 3y.

$740.320

8mo. 4 days

=$152.583

Amount of second payment for 3y.

3mo. 8 days

=89.725

Amount of third payment for 2y.

2mo. 10 days

=169.75

Amount of fourth payment for

11mo. 10 days

=52,833

464.891

275.429

Balance on the 16th of Aug. 1845,

2. A BOND was given for $950, dated March 3d, 1839, on WHICH Were the following endorsements, viz. 1st. April 3d, 1840, $116.28; 2d. July 6th, 1841, $87.50; 3d. Sept. 9th, 1842, $162.50; 4th. June 11th, 1843, $225.18; 5th. Feb. 8th, 1844, $136.48; how much remained due on the 1st of January, 1847, allowing interest at 6 per cent. PER ANNUM? BOND, $950, for 7y. 9mo. 28da., amounts to

1st payment,$116.28, for 6y. 8mo. 28da., amounts to

amount of

payments.

amount of bond.
$1396.183

$163.334

QUESTIONS FOR EXERCISE.

1. A NOTE was given on the 25th of Nov. 1836, for $560, on WHICH the following payments were made, viz. 1st. April 5th, 1837, $100; 2d. July 7th, 1838, $150; 3d. Oct. 11th, 1839, $200, and on the 13th of May, 1840, the balance was paid; what was the last payment?

2. I gave a BOND for $1000, dated Jan. 1st, 1830, on WHICH I made the following payments, viz. 1st. May 3d, 1832, $150; 2d. April 1st, 1834, $162.50; 3d. March 5th, 1836, $175; 4th. June 9th, 1838, $250; 5th. April 17th, 1839, $187.50; how much remained due on the 1st. of Jan. 1840, allowing 6 per cent. interest per YEAR?

3. A. gave B. a NOTE for $436.50, bearing date Aug. 19th, 1825, which B. had the privilege of paying at his convenience; on the 29th of May, 1827, he paid $87.50; on the 20th of Dec., 1828, he paid $90; on the 14th of Jan., 1830, he paid $45.37; on the 23d of May, 1832, he paid $75.16, and on the 1st of January, 1834, he paid the balance; what was the last payment?

4. A BOND for $6845, was dated Feb. 22d, 1839, and had endorsements, as follow: "Received, June 24th, 1840, $650; Jan. 8th, 1841, $468.50; April 7th, 1842, $925.75; June 6th, 1843, $750; Sept. 17th, 1844, $1225; Dec. 9th, 1845, $562.50;" how much remained due on the 1st of April, 1846, allowing interest on the bond and endorsements, at 4 per cent. a YEAR?

COMPOUND INTEREST.

Compound interest is allowable in some countries on the principle that the LENDER, is entitled to his interest annually; therefore, to calculate compound interest, we have the following

RULE.

Find the AMOUNT of the principal for the first year, and make IT the principal for the second year, the AMOUNT of which will form the principal for the third year, &c., the last years' AMOUNT increased by ITs interest for the months and days will be the AMOUNT for the whole time, from WHICH subtract the original principal, the remainder will show the compound INTEREST for the same time.