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3. A tax of $17250 is to be assessed on a town; the real estate is valued at $850000 and the personal property at $250000; there are 500 polls, each of which is taxed $1.50; what is the rate of taxation? Ans. $.015.

4. In a certain school the expenses are as follows: salary of teacher, $500; fuel, $42.75; apparatus, $32.50. The school fund amounted to $125.25, and the rest of the expenses was paid by a rate bill; if the entire attendance was 7280 days, what was C's bill, who sent 4 pupils 90 days each? Ans. $22.25.

MENTAL EXERCISES.
MISCELLANEOUS PROBLEMS.

1. How much currency will $50 in gold buy, when gold is at a premium of 8%?

2. How much gold can be bought for $220 in currency, when gold is at a premium of 10%?

3. If I take 10% off and then another 10% off, what is the rate off?

4. What is the actual rate off, when I take 20% off and then another 20% off?

5. What is the difference between 10% off and 5 and 5% off? between 15% off and 10 and 5% off?

6. What is the difference between 20% off and two 10%'s off? between 10% on and 5 and 5% on?

7. How much is 10 and 10% off? 20 and 10% off? 20 and 5% off? 20 and 20% off? 20 and 20% on ?

8. If an article is sold so as to gain on the cost, what is the gain per cent.?

9. I paid an agent $200 for selling a house for me; what did I receive for it, the rate of commission being 14%?

10. What cost 5 shares of bank stock at 102, brokerage %? 11. Required the cost of $4000 U. S. 44's, at 1084, brokerage %. 12. A boy bought oranges at $3 a hundred, and sold them for 5 cents apiece; what per cent. did he gain?

13. A milliner sold some old-fashioned hats at $3.60, which was 25% below marked price; at what price were they marked?

14. A lady bought some canal stock at 80, and sold it at par, gaining $500; how many shares at $50 each?

15. What per cent. does stock, paying 6% dividends, yield when bought at 90? 8% stocks at 120 ?

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SIMPLE INTEREST.

462. Interest is money charged for the use of money. 463. The Principal is the sum for which interest is charged. Interest is reckoned as a percentage of the principal 464. The Rate of interest is the rate per cent on $1 for a certain time. The usual time is one year.

465. The Time is the period during which the money is on interest.

est.

466. The Amount is the sum of the principal and inter

467. Simple Interest is interest on the principal only. Compound Interest is interest also on the interest. 468. Legal Interest is interest at the rate fixed by law. It varied in different States in 1894 as follows:

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column, the rate that may be

The first column gives the legal rate; second agreed upon; the * indicates no limit to the rate. 469. Usury is a rate of interest greater than the law allows. Various penalties are attached to taking usury.

The legal rate in England and France is 5 %; and in Ireland, Canada, and Nova Scotia is 6%.

In notes, contracts, accounts, mortgages, etc., when no rate is specified, the legal rate is understood.

Notes draw interest after they become due, though interest is not men. tioned in them; and interest is reckoned on book accounts after the expiration of the term of credit.

470. The Quantities are five: 1. The Principal; 2. The Interest; 3. The Rate; 4. The Time; 5. The Amount.

NOTE.-In Computing interest it is customary to reckon a month as of a year, and a day as of a month. In dealing with the U. S. GoverDment, each day is 35 of a year.

CASE I.

471. Given, the principal, the rate per cent., and the time, to find the interest or the amount,

MENTAL EXERCISES.

1. What is the interest of $80 for 2 yr. 6 mo. at 6%?

SCUTION.-6 months equal or of a year, which with 2 yr. equals 21, or years. At 6 per cent. for 1 yr., 18 of the principal equals the Interest, and for 2 or 3 yr., § times 180 or 1 or 2 of the principal equals the interest, of $80 equals $12.

What is the interest of

2. $60 for 6 yr. at 5%?

3. $40 for 4 yr. at 5%?

4. $30 for 5 yr. at 4%?

5. $600 for 2 yr. mo. at 8%?

6. $300 for 4 yr. 6 mo. at 6%?

7. $240 for 3 yr. 9 mo. at 8%?

8. $330 for 7 yr. 6 mo. at 4%?
9. $500 for 3 yr. 7 mo. 6 da, at 5%?

10. What is the interest of $300 for 5 yr. 3 mo. 18 da. at 10%? 11. What is the interest of $500 for 2 yr. 2 mo. 12 da. at 5%? 12. What is the amount of $50 for 2 yr. 8 mo. at 6 per cent.? REMARK. We find that or of the principal equals the interest, hence of the principal equals the amount; } of $50==$58. 13. What is the amount of $600 for 7 yr. 6 mo. at 6 per cent.? 14. What is the amount of $300 for 8 yr. 10 mo. at 6 per cent?

METHOD FOR YEARS.

1. What is the interest of $2400 for 6 yr. 7 mo. 15 da., at 7%

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SOLUTION.-By reduction, we find that 6 yr. 7 mo.

15 da. equals 63 yr. At 7%, .07 times $2400 equals the interest for 1 year, which is $168; if the interest for 1 year is $168, for 63 yr. it is 63 times $168, which by multiplying we find is $1113. Hence the following

OPERATION.

$2400
.07

$168.00

6 $1113.00 Ane

Rule.-I. Multiply the principal by the rate, and that product by the time expressed in years, to find the interest

II. Add the interest to the principal to find the amount.

WRITTEN EXERCISES.

Required the interest

2. Of $360 for 3 yr. 6 mo. at 7%? 3. Of $940 for 7 yr. 8 mo. at 6%? 4. Of $860 for 5 yr. 9 mo. at 5%? 5. Of $780 for 8 yr. 4 mo. at 7%? 6. Of $590 for 3 yr. 10 mo. at 8%?

7. Of $1296 for 5 yr. 10 mo. 15 da. at 6% ? 8. Of $4080 for 3 yr. 3 mo. 9 da. at. 5%?

SIX PER CENT. METHOD.

Ans. $88.20.

Ans. $432.40.
Ans. $247.25.
Ans. $455.
Ans. $180.93.

Ans. $456.84.

Ans. $668.10.

472. The Six Per Cent. Method is so-called because the process is based upon that rate.

1. What is the interest of $240 for 6 yr. 8 mo. 18 da. at 6%?

SOLUTION.-The Int. of $1 for 1 yr. is $0.06,

and for 6 yr. it is 6 times $0.06, or $0.36. The Int. of $1 for 1 mo., or

of 6%, or of a cent, and the Int. for 8 mo.

OPERATION.

of a year, is

6X.06 $0.36

X8

.04

is 8 times of a cent, or $0.04.

18- .003

The Int. of $1 for 1 mo., or 30 da., is

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cent, or 5 mills, and for 1 day it is

of 5

240

$96.72

times of a mill, or $0.003.

mills, or of a mill, and for 18 days it is 18

Adding these results, we have $0.403 as the Int. of $1 for 6 yr. 8 mo. and 18 da., and on $240 it is 240 times $0.403, or $96.72.

Rule.-I. Multiply the rate, .06, by the number of years; take of the number of months as cents, and of the number of days as mills; their sum will be the interest of $1 for the given time at 6%.

II. Multiply this sum by the principal, and the product will be the interest of the principal at 6%. For any other rate, take as many sixths of this interest as the rate is of six.

NOTES.-1. Another method is to reduce the years to months, and take half the number of months for cents, etc., as before.

2. Another method is to take the number of months as cents, and one-third of the uumber of days us mills, and multiply the sum by half the principal. 3. The method for days popularly expressed is, “Multiply dollars by days and divide by 6000,"

WRITTEN EXERCISES.

Required the interest

2. Of $350 for 3 yr. 4 mo. 12 da. at 6%.
3. Of $975 for 5 yr. 6 mo. 6 da. at 6%.
4. Of $834 for 9 yr. 10 mo. 15 da. at 6%.
5. Of $45.95 for 8 yr. 6 mo. 24 da. at 7%.

Ans. $76.76. Ans. $322.724.

Ans. $494.144.

Ans. $27.55+

6. Of $23.75 for 7 yr. 7 mo. 21 da. at 5%. 7. Of $.325 for 9 yr. 5 mo. 14 da. at 8%. 8. $147.37, 4 yr. 11 mo. 13 da., 7%. 9. $635.62, 9 yr. 9 mo. 11 da., 9%. 10. $387.184, 10 yr. 7 mo. 7da., 10%. 11. $570.05, 3 yr. 5 mo. 5 da., 6%. 12 $980.81, 5 yr. 9 mo. 17 da., 7%.

THE 60 DAY METHOD.

Ans. $9.07+. Ans. $.24+. Ans. $51.094. Ans. $559.51+. Ans. $410.53+. Ans. $127.11+.

Ans. $440.66+. .

473. At 6% a year, the rate for 2 mo., or 60 da., is 1% hence for 60 da., Too of the principal equals the interest. From this we have the following method called the 60 Day Method.

Rule.-Point off two places in the principal for the interest for 60 days, and take multiples or aliquot parts of this interest for any other number of days.

1. What is the interest of $360 at 6% for 66 da.? for 96 da.?

SOLUTION.-Pointing off two places we have $3.60, the Int. for 60 da.; then take of $3.60, we have $0.36, the Int. for 6 da.; then the sum of these interests, or $3.96, is the interest for 66 da.

SOLUTION.-Pointing off two places we have $3.60, the Int. for 60 da.; take of $3.60 for the Int. for 30 da.; and of $3.60 for the Int. for 6 da.; their sum is the Int. for 96 da.

OPERATION. $3.60- Int. for 60 da. .36 66 66 6 da.

$3.96

66

"66 da.

OPERATION.

$3.60
1.80

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Int. for 60 da. "30 da.

.36

66

66

6 da.

$5.76-"

96 da.

2. Find the Int. of $720, at 6%, for 6 mo. 12 dá. For 128 da

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