34. On a note of hand for $1,000, payable July 1st, 1835, were received the following indorsements, viz.

Received, April 21st, 1836, $200.
Received, Aug. 6th, 1836, $150.
Received, April 26th, 1837, $300.
Received, Sept. 11th, 1837, $240.
Received, April 1st, 1838, $210.)

Settlement, July 1st, 1839.

Time. 9, 20, 3, 15, 8, 20, 4, 15, 6, 20, 1, 3.

Results. 84833; 71318; 44408; 21407; 11 21.

Answer, $12.05.

EXAMPLES

In which every payment does not exceed the interest then due. 35. On a note given for $600, dated March 1st, 1822, with interest, there were indorsed the following sums.

May 1st, 1823, received $200.
June 16th, 1824, received $ 80.

Sept. 17th, 1825, received $ 12.

Time-1, 2, 1, 1, 15, 1, 8, 15, 1, 7,

Dec. 19th, 1825, received $ 15. (15, 10, 15.

March 1st, 1826, received $100.

Oct. 16th, 1827, received $150.

Settlement, August 31st, 1828. What was the balance due?

36. On a note dated June 16th, 1820, given for $900, with inter est, were indorsed the following payments:

*When the mills are 5 or more, add another cent; but when less than 5, reject them

Time. 1, 15, 1, 2, 15, 2, 11, 1, 6, 15, 1, 6.

Received, July 1st, 1821, $150.
Received, Sept. 16th, 1822, $ 90.
Received, Dec. 10th, 1824, $ 10.
Received, June 1st, 1825, $ 20.
Received, Aug. 16th, 1825, $200.
Received, March 1st, 1827, $300.
Settlement, Sept. 1st, 1828. What was the balance due?

Results. 80,625; 77,470; 68,027, 44,319.

A. $483.08.

(37.) $1,600. For value received, I promise to pay Rufus Stanly, or order, sixteen hundred dollars, with interest.

Albany, July 1st, 1830.

JONATHAN OVERTON. Indorsements.-Received, Oct. 16th, 1830, $200. Jan. 1st, 1831, $200. May 26th, 1831, $500. November 1st, 1831, $15. February 11th, 1832, $25. June 6th, 1832, $11. November 26th, 1832, $11. December 1st, 1832, $5. January 11th, 1833, $24, and the balance November 26th, 1835. What was the balance? Time. 3, 15, 2, 15, 4, 25, 1, 7, 15, 2, 10, 15.

Results. 143,266; 125,355; 78,889; 78,763. A. $946.14.

Established by the Supreme Court of the State of Connecticut in 1804. 38. " Compute the interest to the time of the first payment; if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total. If there be after payments made, compute the interest on the balance due to the next payment, and then deduct the payment as above; and, in like manner, from one payment to another, till all the payments are absorbed; provided the time between one payment and another be one year or more. But if any payments be made before one year's interest hath accrued, then compute the interest on the principal sum due on the obligation, for one year, add it to the principal, and compute the interest on the sum paid, from the time it was paid up to the end of the year; add it to the sum paid, and deduct that sum from the principal and interest, added as above.*"

"If any payments be made of a less sum than the interest arisen at the time of such payment, no interest is to be computed, but only on the principal sum for any period."

39. For value received, I promise to pay Peter Trusty, or order, one thousand dollars, with interest. June 16th, 1824.

$1,000.

INDORSEMENTS.

July 1st, 1825, received $250.

JAMES PAYWELL.

Aug. 16th, 1826, received $157. Time. 1, 15, 1, 1, 15, 1, 8, 15, 6, 6, 10.
Dec. 1st, 1826, received $ 87.

Feb. 16th, 1828, received $218.)

Settlement, Aug. 26th, 1828. What was the balance?

Q. How do you dispose of the first payment by the Connecticut rule? 38. What is to be done with the other payments? 38. What exceptions are men

tioned? 38.

* If a year does not extend beyond the time of payment; but if it does, then find the amount of the principal remaining unpaid, up to the time of settlement, likewise the amount of the payment or payments from the time they were paid to the time of settle ment, and deduct the sum of these several amounts from the amount of the principal.

(40.) $875. For value received, I promise to pay Daniel Bur gess, or order, eight hundred and seventy-five dollars, with interest. Hartford, January 10th, 1821. HENRY FROTHING.

Indorsements.-Received $260, August 10th, 1824. $300, December 16th, 1825. $50, March 1st, 1826. $150, July 1st, 1827. What was there due September 1st, 1828? Time-3, 7, 1, 4, 6, 1, 91, 6, 15, 1, 2. Results-80,313; 56,818; 54,990; 41,777. A. $447.01.

COMPOUND INTEREST.

LXXXII. 1. Compound Interest is the premium given for the use of both the principal and its interest when the latter becomes due and remains unpaid. This is sometimes called interest upon interest. 2. Simple interest implies, as we have seen, (LXXX. 3,) that the interest is payable annually; hence, to find the compound interest, we may proceed as follows: *

RULE.

3. Find the amount of the principal for one year, (unless a different time be named,) then of this amount as before, and so on to the time of settlement.

4. Subtract the given sum from the last amount, and the remainder will be the compound interest required.

LXXXII. Q. What is Compound Interest? 1. What is the rule for finding the amount? 3. What, for finding the compound interest? 4. Why should the interest be compounded annually? 2.

* Compound interest, though just, is not legal.

5. What is the compound interest of $156, for 2 years, and what is the amount?

A. $19.28 1 6=compound interest for two years.

6. What is the compound interest of $500 for 4 years?

A. $131.2384+. 7. What is the compound interest of $15,000 for 5 years at 7 per cent.? A. $6038.275

8. What is the amount of $13,000 for 3 years at compound interest, the rate being 4 per cent.? A. $14835.159.

9. What will $600 amount to at compound interest in 4 years at 7 per cent., the interest being payable semi-annually? Find the amount of $600 for 6 months; then of this amount for another 6 months; and so on for the whole time. A. $790.079.

10. What will be the compound interest of $140 for 3 years, it being payable semi-annually?

A. $27.16. 11. What is the compound interest of $240, payable quarterly, for 2 years, at 7 per cent.? A. $35.728.

12. What is the compound interest of $1,000 for 2 years at 3 per per cent. payable quarterly?

A. $72.18.

13. What is the compound interest of $750 for 5 years and 6 months, payable annually? Find the amount for 5 years, then for 6 months. A. $283.78.

14. What is the amount at compound interest of $300 at 7 per cent. for 3 years 4 months and 15 days? A. $377.15. 15. If a note of $60.60, dated October 25th, 1836, with the interest payable annually, be paid October 25th, 1840, what will it amount to at compound interest? A. $76.51. 16. Find the balance due on the following note, (by LXXXI. 31, 32,) compounding the interest annually.

$1,000. On demand, for value received, I promise to pay John Stearns, or order, one thousand dollars, with interest.

Hartford, August 1st, 1830.

JOSEPH DISCOUNT.

This note has $500 indorsed on the back of it January 16th, 1836, and was paid in full February 1st, 1840. A. $1107.46

17. If the number of colored persons in the United States at the present time (1840) be, as is supposed by some, three millions, and their rate of increase 25 per cent. in ten years, what will be their number in 1860?-in 1900? A. 4,687,500; 11,444,090.

18. As $2 at compound interest amounts to 2 times as much as $1; $3, 3 times as much, and so on, we may make a table containing the amount of £1 or $1 for several years, by which the amount of any sum may be easily found by simply multiplying once.

TABLE,

Showing the amount of £1 or $1, for 30 years at 5, 6, and 7 per cent. compound interest.

19. What is the compound interest of $20.15 for 4 years at 6 per cent. By the Table the amount of $1 for 4 years is $1.262477× $20.15 $25.438+ from which subtracting $20.15 leaves 5.288,7.+ A. $5.288.+ 20. What is the compound interest of $2,000 for ten years at 7 per cent.? A. $1,934.30. At 6 per cent.? A. $1,581.696. At 5 per cent.? A. $1,257.79.

0 2 600

3

207136

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399564

4

603539

4

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4

048935

5

4 29 1870

5

549 38 3

4.8 2 2 3 4 7

111688

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.

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