EQUATION OF PAYMENTS.

SECTION XXII.

243. EQUATION OF PAYMENTS is the process of determining the average time for the payment of several sums, due at different periods.

244. RULE. Multiply each sum by the time before it becomes due, and divide the sum of the products by the sum of the payments.

OBS. 1. This rule has been considered by many as incorrect; but it is as correct as any rule founded upon simple interest can be.

If A owes B $200, $100 of which are to be paid in cash, and the other $100 to be paid in two years, the average time for the payment of the whole, according to the rule, would be one year, which is correct; for it is evident that if the money be paid according to the agreement, B would have at the end of two years $200, and the interest of $100 for two years. If the whole be paid in 1 year, B would have at the end of two years $200, and the interest of $200 for one year, which is the same as the interest of $100 for two years.

OBS. 2. If any sum be paid on the day from which the time is reckoned, it will have no product, but it must be added with the others in finding the sum of the payments.

OBS. 3. It is customary with merchants to add three days grace.

This rule is founded upon the principle that the use of $1 for any number of days is equivalent to the use of as many dollars as there are days for 1 day. Thus, the use of $1 for 150 days is equivalent to the use of $150 for 1 day.

1. A gentleman owes $150, payable in 60 days, $200, payable in 90 days, $400 in 120 days. At what time ought the whole to be paid at once?

What is equation of payments? What is the rule?

EXAMPLES.

2. A owes B $500, of which $100 are to be paid in 4 months, $200 in 6 months, and the remainder in 9 months. What is the average time of payment?

3. A merchant sold the following bills of goods, on a credit of 6 months: May 10, a bill of $600; June 12, a bill of $450; September 20, a bill of $900. At what time will the whole become due ?

4. A gentleman has to pay $5000 as follows: $540 in 4 months, $2400 in 8 months, $600 in 10 months, the remainder in 6 months. What is the average time for the payment of the whole sum?

5. A owes B $1200. $400 are due at the present time, $300 are due in 8 months, and $500 are due in 12 months. At what time ought the whole to be paid?

6. A gentleman left his son $1500, to be paid as follows in 3 months, in 4 months, in 6 months, and the remainder in 8 months. At what time ought the whole to be paid at once?

7. A merchant bought goods amounting to $6000. He agrees to pay $500 in cash, $600 in 6 months, $1500 in 9 months, and the remainder in 10 months. At what time ought he to pay the whole in one pay

ment?

8. A owes B $1600, to be paid in 6 months. A agrees to pay $600 in cash. At what time ought the remainder to be paid?

9. A gentleman purchased a farm for $3600, and agrees to pay $600 down, and the remainder in 5 equal semiannual instalments. At what time may the whole be paid at once?

10. A owes B $5000, to be paid in 30 days, in 3 months, in 70 days, and the remainder in 9 months. At what time ought the whole to be paid at once?

11. A bought goods of B, amounting to $1200. of the bill was to be paid in cash, to be paid in 2 months, the remainder in 9 months. At what time ought the whole to be paid?

245. To find the equated time of payments, when the sums due have different dates,

RULE. Find the time when each sum becomes due, and multiply each sum by the time between it and the first sum that is due, and divide the amount of the several products by the amount of the sums due.

OBS. As the time at which the first sum is due is the period from which the average time is computed, the first sum will have no product.

The principle of this rule is the same as that of the preceding, (ART. 244.)

12. What is the equated time for the payment of the following sums:

38 days from January 10 is February 17, the equat

ed time.

EXAMPLES.

13. A merchant sold 484 barrels of rosin, as follows:

February 6, 4 months' cr., 35 barrels, @ $3.124.

March 12,

What is the equated time for the payment of the whole?

What is the rule to find the equated time of payments, when the sums due have different dates ?

P

14. A merchant sold 1650 barrels of flour, as fol

3 months' cr., 150 barrels, @ $4.50.

August 4,

What is the equated time for the payment of the whole?

15. A merchant sold 576 barrels of rosin, as follows:

May 3,

6 months' cr., 62 barrels, @ $2.50.

What is the equated time for the payment of the

whole ?

TAXES.

SECTION XXIII.

246. A TAX is a certain sum of money assessed on individuals to pay the expenses of government, or of a corporation, society, district, &c.

247. Taxes for paying the expenses of government are usually assessed on the property of individuals, and on male persons without property, when of a certain age. The individual tax is called the poll tax.

OBS. 1. Poll is from a Dutch word, signifying the head. OBS. 2. Every male individual over 20 years of age, is required by the laws of Massachusetts to pay a poll tax.

OBS. 3. Taxable property is of two kinds. viz., real estate and personal property. All property that is unchanging, such as houses, lands, &c., is called real estate. All other property, such as money,

What is a tax? How are taxes usually assessed?

notes, stocks, mortgages, furniture, cattle, &c., is called personal property.

248. To assess a state or other tax,

RULE. Find the amount of all the taxable property, real and personal, and also the number of individuals liable to be taxed. If there be a poll tax, multiply the number of individuals or polls by the amount assessed on each poll, and subtract the product from the sum to be raised. Divide the remainder by the whole amount of taxable property, which will be the tax on one dollar. Multiply the amount of each man's property by the tax on one dollar, and the product will be the tax on his property, which, added to his poll tax, will be his whole tax.

1. A tax of $12,500 is to be assessed upon the inhabitants of a town in which there are 840 ratable polls. The tax on each poll is $1.50. The real and personal property in the town is valued at $5,364,560. What will a man's tax be, whose real estate is valued at $8500, and personal property at $15,000?

56

$12,500-$1260 for poll taxes=$11,240. 12180 002095 on a dollar. This sum, multiplied by the amount of his property, produces $49.2325+$1.50, the poll tax, $50.7325, the required sum.

EXAMPLES.

2. What is a man's tax whose real estate is valued at $25,000, personal $12,500, and 3 polls, in a town where the property is valued at $4,278,560, and the amount assessed is $10,000, there being 750 ratable polls?

3. What will be the amount of a man's tax in the same town, whose property is valued at $75,000? 4. What will be the amount of a man's tax in the same town, whose property is valued at $7320.47 ?

What is the rule to assess a state or other tax?