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167.

PER CENT:

QUESTIONS FOR PRACTICE.

2. What is the amount of $175.62 for one year and six | months, at 6 per cent. ?

175.62 prin.

.06 rate.

10.5372 one yr. int. 1.5 time.

The decimals

526860 below mills are 105372 omitted in the

answer to this

59

10. What is the interest of £86 10s. 4d. for 1 year and 6 months, at 6 per cent.?

86.5166 If the principal .06 be English money, the shillings, pence,

£5.190996 &c. must be reduc1.5 ed to the decimal of a pound, (143),

25954980 then proceed as in 5190996 Federal money. The interest will be

Ans. £7.7864940 in pounds and decimal parts, which must be reInt. 15.80580 and the follow-duced to shillings, &c. (144).

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SECOND METHOD.

ANALYSIS.

168. 1. What is the interest of $60, for 5 months and 21 days, at 18 per cent. per annum?

60 prin. .057 rate.

If the interest of $1 be 12 cents for 12 months, the interest of $1 for 1 month will be 1 cent, for 2 months 2 cents, for 3 months 3 cents-and generally the number of months written as so many cents, or hundredths of a dollar, will be the interest for that time. And as the interest of $1 for Imo. (30 days) is 1 cent, the interest for any number of days is so many 30ths of a cent, or 3ds of a mill. In the present example we write the 5 months as so many cents, or hundredths of a dollar, and di viding the days by 3, find of them to be 7, which we write in the place of mills in the multiplier; and $60 multiplied by $0.057, (the interest of 1 for the given time,) the product, $3.42, is evidently the interest of $60 for that time.

420 300

$3.420 Ans.

169. 2. What is the interest of $60 for 5 months and 21 days, at 6 per cent. per annum?

Since interest at 12 per cent. (168) is found by multiplying by the whole number of months and of the days, interest at 6 per cent. being of 12, may evidently be found by multiplying by half the former multiplier, that is, by half the months written as cents, and one sixth of the days written

2) 60
028

480

120

at the right hand. In the present example, half the months is 2, and if there were no odd days, we should write down 2 cents, 5 mills, or 0.025 for the multiplier; but when there is an odd month and days, as in the present case, it is as well to call the odd month 30 days, and adding thereto the odd days, divide the whole by 6, the quotient (30+21-6-8) will be mills. $0.028 then is the interest of $1 for 5 months 21 days, and 60 times $0.028), or $0.028) times 60, (86)=$1.71, is the interest of $60 for the same time. To multiply 60 by, we take of 60, or divide 60 by 2, and in general for the odd days, less than G, we take such part of the multipl and as the odd days are part of 6. Hence,

30

$1.710 Ans.

170. To compute the interest at 6 per cent. per annum upon any sum for any time.

RULE. Under the principal write half the even number of months, for a multiplier, (pointing them as so many cents, or hundredths of a dollar.) If there be an odd month, call it 30 days, to which add the odd days, if any, and, dividing them by 6, write the quotient in the place of mills in the multiplier. Multiply the principal by this multiplier, and the product, properly pointed, (122) will be the interest for the given time.

NOTI-Odd days less than 6 are so many 6ths of a mill, and to multiply by these, proceed as follows:

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and add the quotient, or quotients, to the product of the principal by half the months.

QUESTIONS FOR PRACTICE.

3. What is the interest of $75, for 4 months and 2 days, at 6 per cent.?

3)751 Here the months is .020.02, and as 6 is not contained in the days, we 1500 write a cipher in the 25 place of mills, that the quotient, in dividing by Ans. $1.525 3, may fall in its proper place. There being 3 decimal places in the factors, there must be 3 pointed off in the product.

4. What is the interest of $215 for 1 month and 15 days?

1mo. 15d. 45d.; 6 in 45, 7 times 2) 215; .007

1505

107

and 3 over.

As there is no even number of months, the two first decimal places must be supplied with ciphers, and 7 must take the place of mills. The use of the ciphers is to guide us in pointing the product.

Ans. $1.612

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171. When the interest is any other than 6 per cent.; first find the interest at 6 per cent., of which take such part as the interest required exceeds, or falls short, of 6 per cent, and this added to, or subtracted from, the interest at 6 per cent., as the case requires, will give the interest required.

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VARIETIES IN SIMPLE INTEREST.

172. 1. What sum of money will amount to $31.35 in 9 months, on interest at 6 per cent.?

As the amount of $1 for 9 months at 6 per cent. is $1.045, the principal, which will produce any other amount at the same rate in the same time, is evidently as many dollars as the number of times $1.045 is contained in that amount, and $31.35-$1.045- $30. Ans. Hence,

I. The time, rate and amount being given, to fired the principal. RULE.-Divide the given amount by the amount of $1 for the given time and rate, and the quotient will be the principal required.

2. The amount for 8 months at 6 per cent. was $598; what was the principal?

Aus. $575.

3. What principal will amount to $1700 in 1 year and 3 months, at 5 per cent.? Ans. $1600.

173. 1. What principal will gain $1.35 in 9 months at 6 per cent.? As $1 in 9 months will gain $0.045, as many dollars will be required to gain $1.35 in 9 months, as the number of times 1.35 contains 0.045 and $1.35 $0.045 $30. Ans. Hence,

II. The time, rate and interest being given, to find the principal. RULE.-Divide the interest, or gain, by the interest of 1 dollar for the given time and rate, and the quotient will be the principal.

2. What principal will gain $23

ia 8 months?

3. What principal will gain $100

Ans. $575. in 1 year and 3 months, at 5 per ct. ?
Ans. $1600.

174 1. If 30 dollars gain 1 dollar 35 cents in 9 months, what is the rate per cent. ?

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Ans. Hence,

III. The principed, istered cut fine bong fra fe tu rok RULE.-Divide the given ingres in the uteres ou fe gives are at one per ceat for the giren ime, aus the quotes will be be a

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175. 1. If the interest on 30 dollars at 6 per ceu per annum, te á dollar and 35 cents, what is the time!

The interest on 30 dollars for 1 year at 5 per cent is 1 dolar and 30 cems. Now, if the given interest be rided by the ineres un the gues principal for one year, the quotient werdendir be the number of years that principal was on interest-315-8145 Brats b the answer. Therefore,

IV. The principal, rate and interest being given, to find the time.

RULE.-Divide the given interest by the interest of the given priaripal for 1 year at the given rate, and the quotient will be the time in years and decimal parts.

2. If the interest on 575 dollars | at 6 per cent. be 23 dollars, what is the time? Ans. 8 months.

3. If the interest of 1600 dollars at 5 per cent. be 100 dollars, what is the time? Ass. 1.25yr=lyr. 38o.

2. Commission and Ensurance.

DEFINITIONS.

176. Commission is an allowance of so much per cent. to an agent for transacting business for another.

Insurance is a contract by which certain persons, or companies, agree to make good losses of property by fire, storms, &c. in consideration of the payment to the insurer of so much per cent. on the value of the property insured.

Premium is the sum paid by the owner of the property for the insurance.

The written contract of insurance is called a policy.

The policy should always cover a sum equal to the estimated value of the property insured, together with the premium; that is, a policy to secure the payment of 100 dollars at 2 per cent. must be made out for 102 dollars.

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