6. A farmer bought of a merchant goods amounting to $175.12, on a credit of 12 months; but paid the debt in 2 months and 10 days. What sum should have been discounted from the debt, allowing the rate of interest to be 8 per cent. ? Ans. $10.59'.

7. A loaned B $320 for 2y. 9m. 25da., at the end of which time the Amount was found to be $383.155'. At what rate per cent. was the interest computed? Ans. 7 per cent.

8. $2500.183.

Philadelphia, June 1st, 1851.

On the 1st day of January, 1852, I promise to pay to William Kind, the sum of Two thousand five hundred dollars, 183 cents, with interest; for value received.

Simon Thankful. Endorsements.-January 1st, 1852, received $1000.

October 10th, 1852, received $35.25.

August 16th, 1853, received $200.

The balance of the Note was not paid until the 1st of January, 1854; what amount was then due?

Ans. $1541.15'.

9. A debt of $375.37, in the District of Columbia, remained unpaid until it had legally amounted to $500. How long was it on interest? Ans. 5.533' years.

10. A gentleman in New York proposes to loan a șum of money which, at lawful interest, shall amount to $5000 in 2 years and 6 months. What must be the amount of the loan? Ans. $4255.319'

11. An account of $200.50 was due, January 1st, 1854. On this debt there was paid, March 10th, $80, and June 20th, $75.25; what balance was due on the 1st of October, 1854, with interest at 6 p. c.? (179). Ans. $50.34'. 12. A merchant bought a stock of goods amounting to $7381.25 on a credit of 6 months, but paid the debt in 3m.

21da. from the time of purchase. What discount should have been allowed him, interest being at 6 per cent. ?

Ans. $83.919'.

13. A debt of $3000.75 will be due in 2y. 7m. 18da. without interest. What sum in hand would be an equivalent for the debt, allowing the rate of interest to be 7 per cent. ? Ans. $2533.77'.

14. An account for $300 was due July 1st, 1854. On this debt there was paid, August 20th, $60, October 15th, $70, and, December 1st, $80. What balance was due on the 1st of January, 1855,—according to each of the two methods which have been given for applying partial payments, with interest at 6 per cent.? Ans. $96.48 and $96.53.

15. A merchant bought 43cwt. 3qr. of sugar, at $5.25 per cwt., which he immediately sold at $7 per cwt., on a credit of 90 days, and then had the purchaser's Note for the amount discounted in Bank, at 6 per cent. What profit did the merchant make? Ans. $71.81'.

16. Wishing to raise the sum of $3760.50, I design, for this purpose, to put a Note in Bank, for 120 days. For what principal must the Note be drawn, interest being at 8 per cent.? Ans. $3866.04'.

17. A owes B 5000; of which $1200 is to be paid in 9 months, $3000 in 1 year and 3 months, and the remainder in 2 years. In what time might the whole debt be paid, without injustice to either? Ans. 15 months.

18. A person owes a debt of $1500, towards the payment of which he is able to raise but $900. He offers this sum, to be applied in part to a payment on the debt, and in part to paying the interest, at 8 per cent., in advance, on his Note, at 12 months, for the remainder. His creditor agreeing, for what principal must the Note be drawn? Ans. $652.17'.

19. A rice plantation was to be paid for as follows: of the purchase money in hand, of it in 12 months, and the remainder in 1 year and 9 months. The parties have since agreed that the whole shall be paid at one time; when should the payment be made? Ans. In 123 months.

20. A person owes a Note of $800 in Bank, and has $500, with which he proposes to pay a part of the Note, and the discount, at 6 per cent., on a Note, at 120 days, to be given for the remainder. How much is he able to pay on the Note? and what will be the discount on the remainder?

Ans. $493.73', and $6.27'.

21. On the 5th of September, 1854, a merchant bought goods to the amount of $5000, on a credit of 6 months. On the 20th of November, he paid $2000 on this debt, and on the 1st of December $1500; to what date might the payment of the balance be equitably deferred ?

Ans. October 25th.

22. A merchant has a customer charged with $48.50 on the 1st of January, $80.25 on the 10th of March, and $100 on the 20th of May, and 6 months credit is allowed on the account. What amout is due on the 1st of December, if interest be charged at 7 per cent., after the account is due? (190). Ans. $231.59'.

23. A held a Note against B for $473.50, due the 3d of April; and B. held one against A for $500.623, due the 10th of June-no interest accruing in either case, until the Note is due. Settlement was had on the 5th of May; what was then the balance between the two, allowing the rate of interest to be 6 per cent. ? Ans. A owed B $21.61'.

24. A merchant bought goods, on the 1st of August, to the amount of $1200, on 3 months credit, on the 10th of September to the amount of $2500, on 4 months' credit, and

on the 20th of October to the amount of $2923, on 6 months' credit. What is the amount of the account on the 1st of January, allowing the rate of interest to be 6 per cent.? (191). Ans. $6583.49'. 25. What would $200 amount to in 3 years, at 6 per cent. compound interest, if the interest be payable annually? (175). Ans. $238.203'.

26. What would $1000 amount to in 2 years, at 8 per cent., compound interest, if the interest were payable semiannually? Ans. $1169.858'.

27. The Debtor side of an Account Current amounts to $325.50, and is due on the 1st of May; the Creditor side amounts to $200, and is due on the 20th of of June. What balance is due on the account on the 1st of August, if interest be at 5 per cent. ? Ans. $128.48'.

28. A speculator buys 320 mules at an average of $621 each, and to pay for them has a Note discounted in Bank, for 120 days, at 6 per cent. In 30 days he sells his mules at an average of $87, and puts the proceeds at interest, at 10 per cent., until his Note is due in Bank; what does he gain by these transactions? Ans. $8304.75'.

29. The Debtor side of an Account Current amounts to $500, and is due on the 10th of August; the Creditor side amounts to $700.50, and is due on the 1st of November. What balance is due on the account on the 20th of September, if interest be at 8 per cent. ? Ans. $190.22'.

30. A merchant took a farmer's Note for $325.50, due, without interest, on the 1st of June, 1852; and some time afterwards the farmer got possession of a Note on the mer*chant for $500, due, without interest, on the 20th of January, 1854. Settlement was had on the 15th of August, 1853 ; how stood the matter of debt between them, interest being at 7 per cent.?

Ans. $132.468' due the farmer.

CHAPTER X.

POWERS AND ROOTS OF NUMBERS.-INVOLUTION AND EVOLUTION.

POWERS AND ROOTS.

(194.) The FIRST POWER of a number is the number itself, thus the first power of 5 is 5.

The second power, or square, of a number, is the product of the number multiplied into itself; thus the second power or square of 5 is 5 × 5, that is, 25.

The third power, or cube, of a number, is the product of the number multiplied into its second power or square; thus the third power, or cube, of 5 is 5 × 5 × 5, that is 125.

What is meant by the fourth power of a number? What is meant by the fifth power of a number? The sixth power of a number? What is the square of 2? What is the cube of 3? What is the square of 4? What is the cube of 6? What is the fourth power of 3?

(195.) The second root, or square root, of a number, is that number whose square is equal to the given number; thus the square root of 9 is 3.

The third root, or cube root, of a number is that number whose cube is equal to the given number; thus the cube root of 8 is 2.

What is meant by the fourth root of a number? What is meant by the fifth root of a number? What is meant by the sixtn root of a number?

What is the square root of 16? What is the cube root of 27? What is the square root of 36? What is the cube root of 1000?

Any power or root whatever of unity is unity, since any number of 1's multiplied together produce 1.

Thus 1×1=1; 1x1x1=1; 1×1x1x1=1; and so on.