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4. What is the interest of 6. What is the interest of £25 $175.62 for 1 year and 6 months, for 6 months, at 4 per cent? at 6 per cent ?

Ans. $15.805.

Ans. 10s. 5. What is the interest of £1 7. What is the amount of 13s. 4d. for 1 year, at 9 per cent? | $10.15 on interest 12 years at 6 Ans. $17.458.

Ans. 3s.

per cent ?

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When there are years, months, and days in the time.

RULE.*-Reduce the months and days to the decimal of a year; find the interest for 1 year by the preceding case, and multiply it by the years with the decimal annexed; the product will be the interest.

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RULE.t-1. Under the principal write 'half the even number of months, (with .5 at the right hand when there is an odd month) for a multiplier, by which multiply the principal and the product, after

*Months are reduced to the decimal of a year by dividing them by 12, and days to the same decimal by dividing them by 360; which is considering the month 30 days, and the year 360, and is generally practised. If greater accuracy is required, find the number of days in the given months and days, and divide them by 365, the quotient will be the true decimal of a year.

+ This rule is a contraction of the Double Rule of Three. Any sum at 6 per cent. simple interest, doubles in 200 months; hence we may say, if $100

removing the separatrix two figures from its natural place towards the left hand, will be the interest in dollars and parts of a dollar.

2. If there be days or an odd month and days in the given time, divide the days (calling the odd month 30) by 6, and place the quotient as a decimal on the right hand of half the even number of months, and proceed as before.

3. If the number of days be less than 6, supply the decimal place with a cipher, and divide the multiplicand according to the following table, and add the quotient to the product. Divide in the same manner, when there is a remainder after dividing the days by 6.

TABLE.

For 1 day,, divide the multiplicand by 6.

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by 3.

66

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by 2.

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by 3 twice.

= and,

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66

by 2 and 3.

in 200 months gain $100, what will a given principal gain in a given number of months? EXAMPLE.-What is the interest of $300 for 8 months, at 6 per cent?

$100 200m. :: $100
300: 8

8

2400
100

100><200=20000)240000(12dolls. Ans.

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Here it will be seen that the three first terms are invariable, and the two last variable quantities; and also that the first and third terms are equal, and therefore cancel each other. Hence we discover that 200 is to any given principal as the number of months in the given time is to the interest. Take the foregoing example. Here it appears that the principal is multiplied by the whole number of months, and divided by 200 for the interest. Now let us divide the third term by the first, and multiply the second term by the quotient (8-200-.04 and $300>< .04 12.) and the result is still the same. Or if we cut off the ciphers

200)2400($12 Ans. as before. in the first term, divide the third

200

400
400

term by 2, and multiply the second term by the quotient, cutting off the two right hand figures of the product 8-2-4, and 300x4=1200) the result is still the same; and this last is precisely the rule, for taking half the number of months is dividing by 2, and removing the separatrix in the product, makes the result the same as if the months had been divided by 200. By this rule, half the even number of months are so many units, one month is therefore, or .5, which is obtamed by dividing 30 days by 6; and if any number of days less than 60 be divided by 6, the quotient may be considered a decimal of a unit, the value of which is 2 months, and may be found to any degree of exactness by annexing ciphers. But since by the rule we obtain only one decimal figure, if there is a remainder, it is necessary to take aliquot parts of the multiplicand for the odd days.

Examples.

1. What is the interest of $275.756, for 1 year, 9 months and 15

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To find the interest for short periods of time, at six per cent.

RULE.-Multiply the principal by the time in days, (calling each year 360, and each month 30 days,) and divide the product by 6;

*This will be found a very convenient practical rule for casting interest for short periods of time, and it is easily remembered. The invention of the rule is similar to the preceding, dividing by 6 and removing the separatrix three figures towards the left hand, being the same as dividing by 6000 days, the number in 200 months, of 30 days each.

the quotient, after removing the separatrix three figures from its natural place towards the left hand, is the interest in dollars and parts of a dollar.

Examples.

1. What is the interest of 17 dollars, 68 cents for 11 months and 28 days?

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When the interest is any other than 6 per cent; first find the interest at 6 per cent. by Case III. or 1V. of which take aliquot parts and add to, or subtract from the interest at 6 per cent. as the case may require.

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To find the interest of any sum by decimals.

RULE.-Multiply the principal by the ratio, and that product by the time; the last product will be the interest required.

Note.

The ratio is the simple interest of $1 for 1 year at the

rate agreed on, thus

At 3 per cent. the ratio is .03

At 4 "

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is .04

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To compute interest on Notes, Bonds, &c.

PRINCIPLES.*-1. If the contract be for the payment of interest annually, the interest becomes due at the end of each year, and if it

*These are the principles on which interest is allowed by the courts of law in Vermont. The following methods are sometimes practised in casting the interest on notes, &c.

1. Find the amount of the principal for the whole time, and also the amount of the endorsements from the time they were made; deduct the later from the former, and the remainder will be the sum due. But this method would be unjust; for, suppose a note be given for $100 with interest, and $6 be paid at the end of each year for 4 years, which is endorsed on the note. Now the interest of the principal for this time is $24, just equal to the sum of the payments; but by this method the several payments all draw interest from the times they are made, the first 3 years, the second 2, and the third 1,= 1 08+.72+ 36— $2.16, which goes towards paying the principal, and in this way any debt would in time be extinguished by the payment of the interest annually.

2. Cast the interest up to the first payment, and if the payment exceed the interest, deduct the excess from the principal and cast the interest on the remainder up to the second payment, and so on. If the payment be less than the inteest, place it by itself, and cast the interest up to the next payment, and so on till the payments exceed the interests, then deduct the excess from the principal, and proceed as before. By this method the interest is supposed to be always due at the time the payment is made. The impropriety of this, as a general rule, may be shown by an example. Supposing A has a note against B for $10000 with interest, payable in one year, and B pays $200 at the end of every 2

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