EQUATION OF PAYMENTS.

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

COMMON RULE.

Multiply each payment by the time before it becomes due, then add the several products together, and divide the total sum by the whole debt; the quotient thence arising will be the equated time required.

PROOF.

The interest of the whole debt payable at the equated time, at any given rate per cent., will be equal to the interest of the several payments for their respective times at the same rate.

3. G is indebted to M in a certain sum, which is to be discharged at 4 separate payments, that is at 2mo. at 4mo. at 6mo. and at 8mo. but they agree to make one payment of the whole; the equated time is therefore required. Ans. 5 months.

4. N bought a quantity of goods on credit, and agreed to pay of the debt every 3mo. until the whole should be discharged, but he afterwards consented to pay it all at once; the equated time is therefore required. Ans. 6 months.

5. W owes Z a certain sum of money, of which is to be paid in hand, at the expiration of 4mo. and the residue at the termination of 8 mo.; I demand the equated time for the payment of the whole debt. Ans. 3 months.

6. X gave his bond to Y for $600, payable at the termination of 8mo. but he is willing to pay Y $200 presently, provided he can have the residue forborne a longer time, to which Y consents; the time of forbearance is therefore demanded. Ans. 12 months.

REBATE OR DISCOUNT.

Discount is an allowance made for the payment of any sum of. money before it becomes due, and is the true difference between the original debt and its present worth in cash.

The present worth of any sum, or debt, due some time hence, is so much present money, which, being put out to interest for that time at the given rate rate per cent. per annum, would amount precisely to the original debt.

RULE.

1. Say-As the months or days in a year

Are to the given rate per cent.;

So is the time proposed

To its interest at that rate.

2. Add the said interest to $100, or £, and call that sum the amount. 3. Say-As the above amount

Is to $100, or pounds;

So is the given sum or debt,

To the present worth required.

4. Subtract the present worth from the given sum, and the remainder will be the discount required.

PROOF.

Find the amount of the present worth at the given rate per cent. per annum, and for the time proposed, which will be equal to the original debt, if the work is right.

N. B. It is believed by many that the interest of the debt for the time before it becomes due, at the stipulated rate per cent. per an

num, is the proper sum to be discounted for the prompt payment thereof. But the following statement and the two first examples will clearly demonstrate the contrary.

THE STATEMEnt.

A owes B the sum of $560, payable 2 years hence, for the prompt payment of which B discounted the interest for the time at $6 per cent. per annum, and therefore received $492.80cts. which he immediately lent to C for the same time, and at the same rate per cent. at the termination of which C paid him $551.93cts. 6-mills, which is $8.06cts. 4 mills less than he would have received from A if the money had remained in his hands till it became due. But, if B had allowed A the true discount only, he would have received $500, which, being put out to interest for 2 years at $6 per cent. per annum, will amount precisely to $560, the original debt.

EXAMPLES.

1. D owes E the sum of $595.20cts. payable at the expiration of 3 years, but he is willing to make prompt payment if E will discount the interest for 3 years, at $8 per cent. per annum, to which E has consented. How much did he lose by allowing the interest instead of the true discount? Examine the work carefully.

$142.84,80 the interest for 3 years which E discounted. 115.20,00=the true discount.

Ans. $27.64, 8 mills. the sum lost by Mr. E.

2. What is the difference between the interest of $1200 for 12 years, at $5 per cent. per annum, and the true discount of the same sum for the said time and rate p. c. p. a. ? Ans. $270.

yr. $ yrs.

1.-As 1 : 5 :: 12

3. What is the present worth of $2652, one half of which is due at the end of 4 months, and the other half at the end of 8 months, discounting at $6 per cent. per annum?

Ans. $2575.

6=1)6-yearly interest.

2=13

1

4 int. of $100 for 8 mo.

100

-2575

104:100:: 1326.. 1275=p.w.

And 1275+1300=2575 the whole present worth required.

4. What sum must I discount for the prompt payment of $2119 50 cents, which is due 2 years hence, at $5.50 cents per cent. per annum? Ans. $210.04cts. 1m.+5100 rem.

5. How much ready money must I have for a bond of $810, due at the end of 3 months, discounting at $5 per cent. p. a.? Ans. $800 6. What is the present worth of $312, one half of which is due in 3 months, and the other half in 6 months, allowing discount at $6 per cent. per annum? Ans. $305.15cts.+. 7. I have sold a tract of land for $2400, one third of which is to

be paid at the end of 1 year, and the residue in two equal annual payments thereafter; what is the present worth of each payment and of the whole debt, allowing discount at $10 per cent. per annum, for prompt payment? Ans. The first payment is $727.27 cents; the second $666.663cts.; the last $615.38cts.+; and the whole present worth is $2009.31 cts.+

8. A man having incautiously sold property on a credit of two years, amounting to $1200, and being suspicious that the obligor will fail before the debt becomes due, is willing to allow a discount of $100 per cent. per annum, for the prompt payment of the resi due; what sum ought he to receive? Ans. $400.

BARTER.

Barter is the exchanging of one commodity for another, and teaches merchants and others to proportion the value, of their respective commodities so that neither of the parties concerned may sustain any loss.

RULE.

Find the value in money of that commodity whose quantity is given, by the shortest method; then find what quantity of the other commodity may be bought with the said value, at the rate proposed. EXAMPLES.

2. How much tea, at 120cts. per lb. must be bartered for 600 lbs. of coffee, at 20cts. per lb. ? Ans. 100lbs. 3. How much wheat, at 125 cents per bushel, must be bartered for 50 bushels of rye, at 70cts. Ans. 28 bushels. per bushel?

4. How much sugar, at 10cts. per lb., must be given in barter for 20cwt. of tobacco, at $10 per cwt.? Ans. 2000lbs.

5. How much sherry wine, at 87 cents per gallon, must be gi ven for 750gals. of Lisbon wine, at 371cts. per gal.? Ans. 321 gals. 6. How much rye, at 70 cents per bushel, will countervail 400 bushels of corn, at 87 cents per bushel? Ans. 500 bushels.

7. How much Madeira wine, at 1624 cents per gallon, must I receive for 325 bushels of corn, at 40cts. per bush.? Ans. 80gals. 8. A has linen at 40 cents per yard, ready money, but in barter he will have 50 cents per yard; B has broadcloth at $4 cash per