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7. What is the present worth of $1000, one-half payable in 8 months, and the other half payable in 8 months after that, at 6 per cent discount? Ans. $943, 73c. 2m.+

8. What is the discount of $1384, of which $500 are payable in 1 year 4 months, and the remainder at the end of 4 years, at 6 per cent? Ans. $208, 13c. 3m.+

EQUATION OF PAYMENTS.

Equation of Payments is the method of finding the mean time to pay at once several debts, due at different times.

RULE.

Multiply each payment by the time at which it is due, then divide the sum of the products by the sum of the payments, and the quotient will be the answer..

EXAMPLES.

1. A owes B $380, to be paid $100 in 6 months, $120 in 7 months, and $160 in 10 months; what is the equated time for the payment of the whole debt

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2. A merchant owes $500, payable as follows; $150 in 4 months; $200 in 6 months, and the rest at 8 months, and he is to make one payment of the whole; I demand the equated time. Ans. 6 months.

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3. A owes B $150, to be paid in 6 months; $180 to be paid in 8 months; $200 to be paid in 10 months, and $250 to be paid in 12 months; what is the equated time for the payment of the whole? Ans. 9 months. 4. What is the equated time for the payment of $1200 of which $500 are payable in 10 months, $400 in 20 months, and the rest in 2 years? Ans. 18 months. 5. A merchant owes $1800, to be paid in 5 months, in 10 months, in 18 months, and the rest in 20 months,

andwishes to pay the whole at once; I demand the equated Ans. 13 months.

time

1. What is Discount?

Questions.

2. What is the present worth of any sum ?

3. (Rules.) How do you find the Discount of any sum?

4. How do you find the present worth?

5. When several sums are payable at different times, how do you find the present worth?

1. What is Equation of Payments ? 2. What is the rule for Equation of Payments?

ANNUITIES AT SIMPLE INTEREST.

An annuity is a sum of money payable every year, or for a certain number of years, or forever.

When the annuity is not paid at the time it becomes due, it is said to be in arrears.

The sum of all the annuities, together with the interest due on each for the time they have been forborne, is called the amount.

1. To find the amount of an Annuity.

RULE.

.1. Cast the interest on the given annuity for one year, then for two years, three years, four years, &c., up to the given time, less 1. Then multiply the annuity by the given number of years, and add the product to the whole interest, and the sum will be the amount required.

EXAMPLES.

J. If an annuity of 200 dollars per annum remain unpaid, (that is, in arrears,) 6 years, what is the amount due, reckoning interest at 6 per cent.?

The interest of $200 for 1 year is

$12,00

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2. If a salary of $325 per year remain unpaid, or in arrears, for the term of 5 years, what amount is then due, interest at 6 per cent? Ans. $1820. 3. If a man, having an annual pension of $75 a year, receive no part of it until the end of 7 years, what is the amount due, interest at 5 per cent? Ans. $603,75.

2. When an annuity is bought off, or paid all at once, at the beginning of the first year, the sum that is paid for it is called the present worth.

To find the present worth of an annuity at Simple Interest.

RULE.

Find the present worth of each year by itself, discounting from the time it falls due, and the sum of all the present worths will be the present worth required.

EXAMPLES.

1. What is the present worth of an annuity of $500, to continue 4 years, at 6 per cent per annum ?

124 100

As 106 100: $500 $471,6981+pres. worth 1st year. 112 100 500: 446,4285+ 118 100 500: 423,7288+ 500:

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2d year.

3d year.

403,2258+

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4th year.

Ans.

$1745,0812=$1745, 8cts. 1,2m.

2. What sum of ready money is equal to an annuity of 100 dollars to continue 3 years, discounting at 6 per cent? Ans. $268,371.

3. What is 600 dollars yearly rent, to continue 4 years, worth in ready money at 6 per cent? Ans. $2094, 09 c. 4. What is the present worth of an annual salary of 800 dollars, to continue 5 years, at 6 per cent?

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Ans. $3407 51,2c.

4. How do you find the amount of an annuity?

5. What is the present worth of an annuity?

6. How do you find the present worth of an annuity?

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TO FIND THE NET WEIGHT OF ANY GOODS OR MERCHANDIZE, WHERE TARE IS ALLOWED.

This is a part of the rule formerly called Tare and Tret, the remainder of which is now become obsolete in the United States, there being no such allowances as Tret. Cloff, &c. now made use of. We shall here notice,

1. Gross weight, which is the whole weight of any kind of goods, including the box, cask, bag, &c. that contains them.

2. Tare, which is an allowance made for the box, cask, bag, &c., which contains them, and is either at so much per box, bag, &c., or at so much per cwt., or at so much on the whole gross weight.

3. Net, which is what remains after the Tare is taken out.

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If the question be an Invoice, add all the gross weights into one sum, and all the tares into another sum; then subtract the whole tare from the whole gross, the remainder will be the net.

EXAMPLES.

1. What is the net weight of 4 hogsheads of sugar marked with the gross weights and tares, as follows?

cwt. qrs.

No. 1, 9

No. 2,

No. 3,

lbs.

lbs.

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No. 4. 8

Whole gross,

Whole tare 371lb.=3

Ans.

1 net.

2. What is the net weight of 5 tierces of rice, No. and

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CASE II.

When the tare is at so much for each box, cask, bag, &c. that contains the goods, multiply the tare of one by the number of boxes, bales, &c., and subtract the product from the gross, the remainder will be the net.

EXAMPLES.

1. In 5 hhds. of sugar, each weighing 9cwt. 3qrs. 17lbs. gross, tare 78lbs. per hogshead, how much net?

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lbs.

17 gross of 1 hogshead.

5

1 gross weight of 5 hogsheads. 26 whole tare of 5 hogsheads.

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3 net.

2. What is the net weight of 12 tubs of butter, each weighing 1cwt. 2qrs. 11lbs., tare per tub 17 pounds? Ans. 17cwt. 1gr. 12lbs. Note. It has now become à general custom and law, to call 100lbs. of almost every article of merchandize a hundred weight, instead of 112lbs. as formerly practiced, and in · the following examples this custom is adopted.

3. In 285 barrels of raisins, each weighing 1cwt. 3qrs. 15lbs., tare per barrel 16lbs., how many pounds net?

Ans. 49590lbs. 4. In 17 bags of coffee, each weighing 97 pounds 5oz., tare per bag 3 pounds 7oz., how much net?

Ans. 15cwt. 3qrs. 20lbs. 14oz. 5. What is the net weight, and value, of 8 hogsheads of tobacco, each 9cwt. 2qrs. 21lbs. gross, tare per hogshead 96 pounds, net at 83 cents per pound?

Ans. Net 7000 pounds. Value $612,50. 6. Sold 15 hogsheads of sugar, each weighing 8cwt. 3qrs. 17lbs., tare per hogshead 45lbs.; required the net weight, and its value at 73 cents per pound.

Ans. Net 12705. Value $984,633.

CASE III.

When the tare is at so much per cwt., divide the given quantity by the aliquot parts of a hundred weight for the

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