4. What is the compound interest of 500 dollars for 4 years, at 6 per cent. per annum? Ans. $131.231. 5. How much will 400L. amount to in 4 years, at 6 per cent. per annum? Ans. 504L. 19s. 94d.

DISCOUNT.

Discount is an allowance made for the payment of a sum of money before it becomes due, according to a certain rate per cent. agreed on between the parties concerned.

The present worth of any debt, not yet due, is so much money as, being put to interest, at a given rate per cent. till the debt become payable, will amount to a sum equal to the debt.

RULE.

Find the amount of 100 pounds, or dollars, at the rate and time given: then,

As the amount of 100 pounds, or dollars,

Is to the given sum, or debt,

So is 100 pounds, or dollars,

To the present worth.

Subtract the present worth from the debt, and the remainder will be the discount.

PROOF.

Find the amount of the present worth for the time and rate proposed, which must equal the given sum or debt.

EXAMPLES.

1. What is the present worth of 590 dollars, due in 3 years, discount at 6 per cent. per annum?

$6 rate
3 years

18

100

118 amt. of $100.

Ans. 500 dollars.

2. What is the discount of 795L. 11s. 2d. for 11 months, at 6 per cent. per annum?

Ans. 41L. 9s. 6d.

105 10 795 11 2:: 100: 754 1 8 present worth. 3. What is the present worth of 672L. due in 2 years; discount at 6 per cent. per annum? Ans. 600L. 4. What is the present worth of 308L. 15s. due in 18 months; discount at 8 per cent, per annum?

Ans. 275L. 13s. 4 d. 5. What is the present worth of $430.67, due in 19 months; discount at 5 per cent. per annum?

Ans. $399.07. 6. What is the discount of 112L. 12s. due in 20 months, at 7 per cent. per annum? Ans. 11L. 15s. 3 d. 7. What is the present worth of 100L. one half due in 4 months, and the other half in 8 months; discount at 5 per cent. per annum? Ans. 97L. 11s. 4d. S. Bought goods amounting to $615.75, at 6 months) credit; how much ready money must be paid, if a discount of 4 per cent. per annum be allowed?

Ans. $602.20. 9. What is the difference between the interest of 1204 dollars at 5 per cent. per annum for 8 years; and the discount of the same sum for the same time and rate per cent.? Ans. $137.60. Note.-Discount for present payment is often made without regard to time; it is then found precisely as the interest of the given sum for 1 year.

EXAMPLES.

1. How much is the discount of 853 dollars, at 2 per cent.? Ans. $17.06.

853
2

17.06

2. How much is the discount of 750 dollars, at 3 per

cent.?

Ans. $22.50.

3. How much is the discount of 650L. at 4 per cent.? Ans. 26L. 4. Bought goods on credit, amounting to 1656 dollars; how much ready morey must be paid for them, if a discount of 5 per cent. be allowed? Ans. $1573.20. 5. A holds B's note for 175L. 10s. he agrees to allow B a discount of 3 per cent. for present payment; what sum must B pay? Ans. 170L. 4s. 8d.

EQUATION.

Equation is a method of reducing several stated times, at which money is payable, to one mean or equated time.

RULE.

Multiply each payment by its time, add the several products together, and divide the sum by the whole debt; the quotient will be the equated time.

PROOF.

The interest of the sum payable at the equated time, at any given rate, will equal the interest of the several payments, for their respective times, at the same rate.

EXAMPLES.

1. Cowes D 100 dollars, of which 50 dollars is to be paid at 2 months, and 50 at 4 months; but they agree that the whole shall be paid at one time, when must it be paid? Ans. 3 months.

50×2=100
50×4=200

100)3100

3 months.

2. A owes B 380L. of which 100L. is to be paid at 6 months, 120L. at 7 months, and 160L. at 10 months; but they agree that the whole shall be paid at one time: when must it be paid? Ans. at 8 months. 3. A merchant has owing to him 300L. to be paid as

follows: 50L. at 2 months, 100L. at 5 months, and 150L. at 8 months; it is agreed to make one payment of the whole: at what time must it be paid? Ans. 6 months.

4. F owes H 2400 dollars, of which 480 dollars are to be paid at present, 960 dollars at 5 months, and the rest at 10 months, but they agree to make one payment of the whole, and wish to know the time.

Ans. 6 months. 5. A merchant has purchased goods to the amount of 2000 dollars, of which sum 400 dollars are to be paid at present, 800 dollars at 6 months, and the rest at 9 months; but it is agreed to make one payment of the whole: what is the equated time? Ans. 6 months. 6. G owes K 420L. which will be due 6 months hence: it is agreed that 60L. shall be paid now, and that the rest remain unpaid a longer time than 6 months; when must it be paid? Ans. in 7 months.

BARTER.

Barter is the exchanging of one commodity for another, according to the price or value agreed upon by the parties concerned.

Questions relating to barter are solved, either by the Rule of Three or by Practice.

Note. When a given quantity of any commodity at a given price, is to be bartered for another commodity at a given price, find the value, in money, of that commodity whose quantity is given; then find what quantity of the other may be had for that value.

EXAMPLES.

1. How much sugar at 11d. per lb. must be given in barter for 1100lb. of rice, at 34d. per lb.? Ans. 350lb.

2. How much sugar at 9d. per lb. must be given in barter for 492lb. of rice, at 3d. per lb.? Ans. 164lb. 3. How much tea at 64 cents per lb. must be given in barter for 448lb. of coffee, at 20 cents

per lb.? Ans. 140lb. 4. What quantity of tea, at 10s. per lb. must be given for 720lb. of chocolate, at 4s. 2d. per lb.?

Ans. 300lb. 5. How much wheat at Idol. 25cts. per bushel, is equal in value to 50 bushels of rye, at 70 cents per bushel? Ans. 28 bushels. 6. B has 75 yards of muslin, at 1s. 4d. per yard, which he is to give to H for linen, at 5s. per yard; how much linen will he receive? Ans. 20 yards. 7. A has sugar at 9d. per lb. for a quantity of which F is to give him 225lb. of tea, at 6s. per lb.; how much sugar must F receive for his tea?

Ans. 1800lb. 8. How much sugar at 8d. per lb. must be given in barter for 20cwt. of tobacco, at 3L.

per cwt.? Ans. 16cwt. Oqrs. 8lb. 9. A merchant has 1000 yards of canvas, at 94d. per yard, which he is to barter for serge, at 104d. per yard; how many yards of serge should he receive?

10. A grocer bartered 5cwt. of for cinnamon at 10s. 8d. per did he receive?

lb.;

Ans. 926 yards.

sugar at 6d. per lb. how much cinnamon Ans. 26lb. 4oz.

11. A has 41cwt. of hops, at 30s. per cwt. for which B is to give him 20L. in money, and the rest in prunes, at 5d. per lb.: what quantity of prunes must A receive? Ans. 1992lb.

12. A and B barter: A has 320lb. of chocolate, at 4s. 6d. per lb. for which B is to give him 30L. in money, and the rest in cotton at 8d. per lb. How much cotton is B to give A? Ans. 1260lb.

13. L has 41cwt. of hops, at 4dols. 50cts. per cwt. for which M is to give him 28dols. 50cts. in money, and the rest in salt, at 80cts. per bushel; what quantity of salt is M to give L.? Ans. 195 bushels.

14. G has 284lb. of tea, at 11s. 6d. per lb. for which B is to give him 40 yards of linen, at 7s. 4d. per yard, and the rest in money; how much money must G receive? Ans. 1L. 14s. 5d.