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QUESTIONS FOR PRACTICE.

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10. What is the interest of £86 10s. 4d. for 1 year and 6 months, at 6 per cent.? 86.5166 If the principal be .06 English money, the shillings, pence, &c.

£5.199996 must be reduced to 1.5 the decimal of a pound, (143.) then 25954980 proceed as in Feder5190996 al money. The interest will be in Ans.7.78649401 pounds and decimal parts, which must be reduced to shillings, &c. (144)

11. What is the interest of

£1 13s. 4d. for 1 year, at 9 per cent.?

Ans. 3s.

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SECOND METHOD.

ANALYSIS.

168. 1. What is the interest of $60, for 5 months and 21 days, at 12 per cent. per annum ?

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

60. prin. .057 rate.

420 300

$3.420 Ans. of $1 for the given $60 for that time,

for 1mo. (30 days) is 1 cent, the interest för 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 dividing the days by 3, find 1 of them to be 7, which we write in the place of mills in the multiplier; and $60 multiplied by $0.057, (the interest time,) the product, $3.42, is evidently the interest of

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 2) 60.

.028

480

120

30

days written at the right hand. In the present example half the months is 22, and if there were no odd days, we should write down 2cts. 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 $1.710 Ans. 6-8) will be mills. $0.028 then is the interest of $1 for 5 mo. 21d. and 60 times $0.0284, or $0.0282 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 6, we take such part of the multiplicand as the odd days are part of 6. Hence,

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.

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

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by 2 and 3

For 5 66 ==

and add the quotient, or quotients, to the product of the prin

cipal 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)75 Here the months is
.020 .02, and as 6 is not con-

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tained in the days, we 1500 write a cipher in the 25 place of mills, that the

quotient, în dividing by An $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? Imo. 15d.-45d. 6 in 45, 7 times

and 3 over.

2)215 As there is no even 007 number of months, the two first decimal places 1505 must be supplied with 107 ciphers, and 7 must take the place of mills. The Ans. $1.612 use of the ciphers is to guide us in pointing the product.

5. What is the interest of $275.756, for 1 year, 9 months and 15 days? Ans. $29.643.

6. What is the interest of

$137.84 for 2 years and 6 months? Ans. $20.676.

7. What is the interest of $575 for 8 months?

Ans. $23.

8. What is the interest of $13.41 for 3 months and 16 Ans. $0.236.

days?

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2 10 7 Time.

$212 on interest for 14 months? 11. What is the amount of Ans. $226.84.

12. A note for $27.55 on interest, was dated Feb. 14, 1823; what was there due, principal and interest, Jan. 20, 1824? Ans. $29.092.

$87.91 on interest 3 years and 13. What is the amount of 27 days? Ans. $104.129.

14. What is the interest of

$607.50 for 5 years?

Ans. $182.25.

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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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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 find 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?

Ans. $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 $0.045-830. 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 dolls. in 8 months?

Ans. $575.

3. What principal will gain 100 dolls. in 1 year and 3 months, at 5 per cent. ? Ans. 1600 dolls.

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

At 1 per cent for the given time, 30 dolls. will gain 22 cents 5 mills, the rate therefore is so many times 1 per cent. as 22 cents 5 mills is contained in the whole gain, which is $1.35, i. e. $1.35÷$0.225 .06, or 6 per cent. Ans.

Hence,

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

RULE.-Divide the given interest by the interest on the given principal, at one per cent. for the given time, and the quotient will be the rate per

cent.

2. If the interest on 573 dollars for 8 months be 23 dollars, what is the rate per cent.?

Ans. 6 per cent.

3. If the interest of 1600 dollars for 1 year and 3 months, be 100 dollars, what is the rate?

Ans. 5 per cent.

175. 1. If the interest on 30 dollars at 6 per cent. per annum, be 1 dollar and 35 cents, what is the time?

cents.

The interest on 30 dollars for 1 year at 6 per cent. is 1 dollar and 80 Now if the given interest be divided by the interest on the given principal for one year, the quotient will evidently be the number of years that principal was on interest-$1.35÷$1.80=0.75yr. 4 months, (145) Therefore,

the answer.

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

RULE.-Divide the given interest by the interest of the given princi pal 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?

Ans. 1.25yr. 1yr. 3mo.

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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